Solve for c (complex solution)
\left\{\begin{matrix}c=\frac{1}{e}\approx 0.367879441\text{, }&x\neq -\frac{3}{2}\\c\in \mathrm{C}\text{, }&x=-\frac{3}{2}\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{3}{2}\text{, }&c\neq \frac{1}{e}\\x\in \mathrm{C}\text{, }&c=\frac{1}{e}\end{matrix}\right.
Solve for c
\left\{\begin{matrix}c=\frac{1}{e}\approx 0.367879441\text{, }&x\neq -\frac{3}{2}\\c\in \mathrm{R}\text{, }&x=-\frac{3}{2}\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{3}{2}\text{, }&c\neq \frac{1}{e}\\x\in \mathrm{R}\text{, }&c=\frac{1}{e}\end{matrix}\right.
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3ce\left(3+2x\right)-7=30x-2\left(12x-1\right)
Multiply both sides of the equation by 6, the least common multiple of 2,6,3.
9ec+6ecx-7=30x-2\left(12x-1\right)
Use the distributive property to multiply 3ce by 3+2x.
9ec+6ecx-7=30x-24x+2
Use the distributive property to multiply -2 by 12x-1.
9ec+6ecx-7=6x+2
Combine 30x and -24x to get 6x.
9ec+6ecx=6x+2+7
Add 7 to both sides.
9ec+6ecx=6x+9
Add 2 and 7 to get 9.
\left(9e+6ex\right)c=6x+9
Combine all terms containing c.
\left(6ex+9e\right)c=6x+9
The equation is in standard form.
\frac{\left(6ex+9e\right)c}{6ex+9e}=\frac{6x+9}{6ex+9e}
Divide both sides by 9e+6ex.
c=\frac{6x+9}{6ex+9e}
Dividing by 9e+6ex undoes the multiplication by 9e+6ex.
c=\frac{1}{e}
Divide 6x+9 by 9e+6ex.
3ce\left(3+2x\right)-7=30x-2\left(12x-1\right)
Multiply both sides of the equation by 6, the least common multiple of 2,6,3.
9ec+6exc-7=30x-2\left(12x-1\right)
Use the distributive property to multiply 3ce by 3+2x.
9ec+6exc-7=30x-24x+2
Use the distributive property to multiply -2 by 12x-1.
9ec+6exc-7=6x+2
Combine 30x and -24x to get 6x.
9ec+6exc-7-6x=2
Subtract 6x from both sides.
6exc-7-6x=2-9ec
Subtract 9ec from both sides.
6exc-6x=2-9ec+7
Add 7 to both sides.
6exc-6x=9-9ec
Add 2 and 7 to get 9.
\left(6ec-6\right)x=9-9ec
Combine all terms containing x.
\frac{\left(6ec-6\right)x}{6ec-6}=\frac{9-9ec}{6ec-6}
Divide both sides by 6ec-6.
x=\frac{9-9ec}{6ec-6}
Dividing by 6ec-6 undoes the multiplication by 6ec-6.
x=-\frac{3}{2}
Divide 9-9ec by 6ec-6.
3ce\left(3+2x\right)-7=30x-2\left(12x-1\right)
Multiply both sides of the equation by 6, the least common multiple of 2,6,3.
9ec+6ecx-7=30x-2\left(12x-1\right)
Use the distributive property to multiply 3ce by 3+2x.
9ec+6ecx-7=30x-24x+2
Use the distributive property to multiply -2 by 12x-1.
9ec+6ecx-7=6x+2
Combine 30x and -24x to get 6x.
9ec+6ecx=6x+2+7
Add 7 to both sides.
9ec+6ecx=6x+9
Add 2 and 7 to get 9.
\left(9e+6ex\right)c=6x+9
Combine all terms containing c.
\left(6ex+9e\right)c=6x+9
The equation is in standard form.
\frac{\left(6ex+9e\right)c}{6ex+9e}=\frac{6x+9}{6ex+9e}
Divide both sides by 9e+6ex.
c=\frac{6x+9}{6ex+9e}
Dividing by 9e+6ex undoes the multiplication by 9e+6ex.
c=\frac{1}{e}
Divide 6x+9 by 9e+6ex.
3ce\left(3+2x\right)-7=30x-2\left(12x-1\right)
Multiply both sides of the equation by 6, the least common multiple of 2,6,3.
9ec+6exc-7=30x-2\left(12x-1\right)
Use the distributive property to multiply 3ce by 3+2x.
9ec+6exc-7=30x-24x+2
Use the distributive property to multiply -2 by 12x-1.
9ec+6exc-7=6x+2
Combine 30x and -24x to get 6x.
9ec+6exc-7-6x=2
Subtract 6x from both sides.
6exc-7-6x=2-9ec
Subtract 9ec from both sides.
6exc-6x=2-9ec+7
Add 7 to both sides.
6exc-6x=9-9ec
Add 2 and 7 to get 9.
\left(6ec-6\right)x=9-9ec
Combine all terms containing x.
\frac{\left(6ec-6\right)x}{6ec-6}=\frac{9-9ec}{6ec-6}
Divide both sides by 6ec-6.
x=\frac{9-9ec}{6ec-6}
Dividing by 6ec-6 undoes the multiplication by 6ec-6.
x=-\frac{3}{2}
Divide 9-9ec by 6ec-6.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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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}