Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{\left(x-2\right)\left(x+1\right)}{6hk\left(x+2\right)}\text{, }&h\neq 0\text{ and }x\neq -2\text{ and }k\neq 0\\a\in \mathrm{C}\text{, }&\left(x=2\text{ and }k=0\right)\text{ or }\left(x=2\text{ and }h=0\right)\text{ or }\left(x=-1\text{ and }k=0\right)\text{ or }\left(x=-1\text{ and }h=0\right)\end{matrix}\right.
Solve for h (complex solution)
\left\{\begin{matrix}h=\frac{\left(x-2\right)\left(x+1\right)}{6ak\left(x+2\right)}\text{, }&a\neq 0\text{ and }x\neq -2\text{ and }k\neq 0\\h\in \mathrm{C}\text{, }&\left(x=2\text{ and }k=0\right)\text{ or }\left(x=2\text{ and }a=0\right)\text{ or }\left(x=-1\text{ and }k=0\right)\text{ or }\left(x=-1\text{ and }a=0\right)\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{\left(x-2\right)\left(x+1\right)}{6hk\left(x+2\right)}\text{, }&h\neq 0\text{ and }x\neq -2\text{ and }k\neq 0\\a\in \mathrm{R}\text{, }&\left(x=2\text{ and }k=0\right)\text{ or }\left(x=2\text{ and }h=0\right)\text{ or }\left(x=-1\text{ and }k=0\right)\text{ or }\left(x=-1\text{ and }h=0\right)\end{matrix}\right.
Solve for h
\left\{\begin{matrix}h=\frac{\left(x-2\right)\left(x+1\right)}{6ak\left(x+2\right)}\text{, }&a\neq 0\text{ and }x\neq -2\text{ and }k\neq 0\\h\in \mathrm{R}\text{, }&\left(x=2\text{ and }k=0\right)\text{ or }\left(x=2\text{ and }a=0\right)\text{ or }\left(x=-1\text{ and }k=0\right)\text{ or }\left(x=-1\text{ and }a=0\right)\end{matrix}\right.
Graph
Share
Copied to clipboard
x^{2}-x-2=3k\left(4+2x\right)ha
Use the distributive property to multiply x-2 by x+1 and combine like terms.
x^{2}-x-2=\left(12k+6kx\right)ha
Use the distributive property to multiply 3k by 4+2x.
x^{2}-x-2=\left(12kh+6kxh\right)a
Use the distributive property to multiply 12k+6kx by h.
x^{2}-x-2=12kha+6kxha
Use the distributive property to multiply 12kh+6kxh by a.
12kha+6kxha=x^{2}-x-2
Swap sides so that all variable terms are on the left hand side.
\left(12kh+6kxh\right)a=x^{2}-x-2
Combine all terms containing a.
\left(6hkx+12hk\right)a=x^{2}-x-2
The equation is in standard form.
\frac{\left(6hkx+12hk\right)a}{6hkx+12hk}=\frac{\left(x-2\right)\left(x+1\right)}{6hkx+12hk}
Divide both sides by 12kh+6khx.
a=\frac{\left(x-2\right)\left(x+1\right)}{6hkx+12hk}
Dividing by 12kh+6khx undoes the multiplication by 12kh+6khx.
a=\frac{\left(x-2\right)\left(x+1\right)}{6hk\left(x+2\right)}
Divide \left(-2+x\right)\left(1+x\right) by 12kh+6khx.
x^{2}-x-2=3k\left(4+2x\right)ha
Use the distributive property to multiply x-2 by x+1 and combine like terms.
x^{2}-x-2=\left(12k+6kx\right)ha
Use the distributive property to multiply 3k by 4+2x.
x^{2}-x-2=\left(12kh+6kxh\right)a
Use the distributive property to multiply 12k+6kx by h.
x^{2}-x-2=12kha+6kxha
Use the distributive property to multiply 12kh+6kxh by a.
12kha+6kxha=x^{2}-x-2
Swap sides so that all variable terms are on the left hand side.
\left(12ka+6kxa\right)h=x^{2}-x-2
Combine all terms containing h.
\left(6akx+12ak\right)h=x^{2}-x-2
The equation is in standard form.
\frac{\left(6akx+12ak\right)h}{6akx+12ak}=\frac{\left(x-2\right)\left(x+1\right)}{6akx+12ak}
Divide both sides by 12ka+6kax.
h=\frac{\left(x-2\right)\left(x+1\right)}{6akx+12ak}
Dividing by 12ka+6kax undoes the multiplication by 12ka+6kax.
h=\frac{\left(x-2\right)\left(x+1\right)}{6ak\left(x+2\right)}
Divide \left(-2+x\right)\left(1+x\right) by 12ka+6kax.
x^{2}-x-2=3k\left(4+2x\right)ha
Use the distributive property to multiply x-2 by x+1 and combine like terms.
x^{2}-x-2=\left(12k+6kx\right)ha
Use the distributive property to multiply 3k by 4+2x.
x^{2}-x-2=\left(12kh+6kxh\right)a
Use the distributive property to multiply 12k+6kx by h.
x^{2}-x-2=12kha+6kxha
Use the distributive property to multiply 12kh+6kxh by a.
12kha+6kxha=x^{2}-x-2
Swap sides so that all variable terms are on the left hand side.
\left(12kh+6kxh\right)a=x^{2}-x-2
Combine all terms containing a.
\left(6hkx+12hk\right)a=x^{2}-x-2
The equation is in standard form.
\frac{\left(6hkx+12hk\right)a}{6hkx+12hk}=\frac{\left(x-2\right)\left(x+1\right)}{6hkx+12hk}
Divide both sides by 12kh+6khx.
a=\frac{\left(x-2\right)\left(x+1\right)}{6hkx+12hk}
Dividing by 12kh+6khx undoes the multiplication by 12kh+6khx.
a=\frac{\left(x-2\right)\left(x+1\right)}{6hk\left(x+2\right)}
Divide \left(-2+x\right)\left(1+x\right) by 12kh+6khx.
x^{2}-x-2=3k\left(4+2x\right)ha
Use the distributive property to multiply x-2 by x+1 and combine like terms.
x^{2}-x-2=\left(12k+6kx\right)ha
Use the distributive property to multiply 3k by 4+2x.
x^{2}-x-2=\left(12kh+6kxh\right)a
Use the distributive property to multiply 12k+6kx by h.
x^{2}-x-2=12kha+6kxha
Use the distributive property to multiply 12kh+6kxh by a.
12kha+6kxha=x^{2}-x-2
Swap sides so that all variable terms are on the left hand side.
\left(12ka+6kxa\right)h=x^{2}-x-2
Combine all terms containing h.
\left(6akx+12ak\right)h=x^{2}-x-2
The equation is in standard form.
\frac{\left(6akx+12ak\right)h}{6akx+12ak}=\frac{\left(x-2\right)\left(x+1\right)}{6akx+12ak}
Divide both sides by 12ka+6kax.
h=\frac{\left(x-2\right)\left(x+1\right)}{6akx+12ak}
Dividing by 12ka+6kax undoes the multiplication by 12ka+6kax.
h=\frac{\left(x-2\right)\left(x+1\right)}{6ak\left(x+2\right)}
Divide \left(-2+x\right)\left(1+x\right) by 12ka+6kax.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}