Solve for x (complex solution)
\left\{\begin{matrix}x=-2a\text{, }&a\neq 2\text{ and }a\neq 0\\x\in \mathrm{C}\text{, }&a=-2\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-2a\text{, }&a\neq 2\text{ and }a\neq 0\\x\in \mathrm{R}\text{, }&a=-2\end{matrix}\right.
Solve for a
\left\{\begin{matrix}\\a=-2\text{, }&\text{unconditionally}\\a=-\frac{x}{2}\text{, }&x\neq -4\text{ and }x\neq 0\end{matrix}\right.
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-4\left(x+2a\right)-\left(a-2\right)x=2a\left(a-2\right)
Multiply both sides of the equation by 4a\left(a-2\right), the least common multiple of 2a-a^{2},4a,2.
-4x-8a-\left(a-2\right)x=2a\left(a-2\right)
Use the distributive property to multiply -4 by x+2a.
-4x-8a-\left(ax-2x\right)=2a\left(a-2\right)
Use the distributive property to multiply a-2 by x.
-4x-8a-ax+2x=2a\left(a-2\right)
To find the opposite of ax-2x, find the opposite of each term.
-2x-8a-ax=2a\left(a-2\right)
Combine -4x and 2x to get -2x.
-2x-8a-ax=2a^{2}-4a
Use the distributive property to multiply 2a by a-2.
-2x-ax=2a^{2}-4a+8a
Add 8a to both sides.
-2x-ax=2a^{2}+4a
Combine -4a and 8a to get 4a.
\left(-2-a\right)x=2a^{2}+4a
Combine all terms containing x.
\left(-a-2\right)x=2a^{2}+4a
The equation is in standard form.
\frac{\left(-a-2\right)x}{-a-2}=\frac{2a\left(a+2\right)}{-a-2}
Divide both sides by -2-a.
x=\frac{2a\left(a+2\right)}{-a-2}
Dividing by -2-a undoes the multiplication by -2-a.
x=-2a
Divide 2a\left(2+a\right) by -2-a.
-4\left(x+2a\right)-\left(a-2\right)x=2a\left(a-2\right)
Multiply both sides of the equation by 4a\left(a-2\right), the least common multiple of 2a-a^{2},4a,2.
-4x-8a-\left(a-2\right)x=2a\left(a-2\right)
Use the distributive property to multiply -4 by x+2a.
-4x-8a-\left(ax-2x\right)=2a\left(a-2\right)
Use the distributive property to multiply a-2 by x.
-4x-8a-ax+2x=2a\left(a-2\right)
To find the opposite of ax-2x, find the opposite of each term.
-2x-8a-ax=2a\left(a-2\right)
Combine -4x and 2x to get -2x.
-2x-8a-ax=2a^{2}-4a
Use the distributive property to multiply 2a by a-2.
-2x-ax=2a^{2}-4a+8a
Add 8a to both sides.
-2x-ax=2a^{2}+4a
Combine -4a and 8a to get 4a.
\left(-2-a\right)x=2a^{2}+4a
Combine all terms containing x.
\left(-a-2\right)x=2a^{2}+4a
The equation is in standard form.
\frac{\left(-a-2\right)x}{-a-2}=\frac{2a\left(a+2\right)}{-a-2}
Divide both sides by -2-a.
x=\frac{2a\left(a+2\right)}{-a-2}
Dividing by -2-a undoes the multiplication by -2-a.
x=-2a
Divide 2a\left(2+a\right) by -2-a.
Examples
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{ 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}