Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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-4x-12+x=3\left(x+2\right)-18-6x
Use the distributive property to multiply -4 by x+3.
-3x-12=3\left(x+2\right)-18-6x
Combine -4x and x to get -3x.
-3x-12=3x+6-18-6x
Use the distributive property to multiply 3 by x+2.
-3x-12=3x-12-6x
Subtract 18 from 6 to get -12.
-3x-12=-3x-12
Combine 3x and -6x to get -3x.
-3x-12+3x=-12
Add 3x to both sides.
-12=-12
Combine -3x and 3x to get 0.
\text{true}
Compare -12 and -12.
x\in \mathrm{C}
This is true for any x.
-4x-12+x=3\left(x+2\right)-18-6x
Use the distributive property to multiply -4 by x+3.
-3x-12=3\left(x+2\right)-18-6x
Combine -4x and x to get -3x.
-3x-12=3x+6-18-6x
Use the distributive property to multiply 3 by x+2.
-3x-12=3x-12-6x
Subtract 18 from 6 to get -12.
-3x-12=-3x-12
Combine 3x and -6x to get -3x.
-3x-12+3x=-12
Add 3x to both sides.
-12=-12
Combine -3x and 3x to get 0.
\text{true}
Compare -12 and -12.
x\in \mathrm{R}
This is true for any x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}