Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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\left(x^{2}+3x+2\right)\left(x+3\right)=x^{3}+6x^{2}+11x+6
Use the distributive property to multiply x+1 by x+2 and combine like terms.
x^{3}+6x^{2}+11x+6=x^{3}+6x^{2}+11x+6
Use the distributive property to multiply x^{2}+3x+2 by x+3 and combine like terms.
x^{3}+6x^{2}+11x+6-x^{3}=6x^{2}+11x+6
Subtract x^{3} from both sides.
6x^{2}+11x+6=6x^{2}+11x+6
Combine x^{3} and -x^{3} to get 0.
6x^{2}+11x+6-6x^{2}=11x+6
Subtract 6x^{2} from both sides.
11x+6=11x+6
Combine 6x^{2} and -6x^{2} to get 0.
11x+6-11x=6
Subtract 11x from both sides.
6=6
Combine 11x and -11x to get 0.
\text{true}
Compare 6 and 6.
x\in \mathrm{C}
This is true for any x.
\left(x^{2}+3x+2\right)\left(x+3\right)=x^{3}+6x^{2}+11x+6
Use the distributive property to multiply x+1 by x+2 and combine like terms.
x^{3}+6x^{2}+11x+6=x^{3}+6x^{2}+11x+6
Use the distributive property to multiply x^{2}+3x+2 by x+3 and combine like terms.
x^{3}+6x^{2}+11x+6-x^{3}=6x^{2}+11x+6
Subtract x^{3} from both sides.
6x^{2}+11x+6=6x^{2}+11x+6
Combine x^{3} and -x^{3} to get 0.
6x^{2}+11x+6-6x^{2}=11x+6
Subtract 6x^{2} from both sides.
11x+6=11x+6
Combine 6x^{2} and -6x^{2} to get 0.
11x+6-11x=6
Subtract 11x from both sides.
6=6
Combine 11x and -11x to get 0.
\text{true}
Compare 6 and 6.
x\in \mathrm{R}
This is true for any x.
Examples
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Matrix
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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}