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12+13x-2x^{2}
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12+13x-2x^{2}
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3x^{2}-\left(3x^{2}-5x-2\right)-2\left(x+1\right)\left(x-5\right)
Use the distributive property to multiply x-2 by 3x+1 and combine like terms.
3x^{2}-3x^{2}+5x+2-2\left(x+1\right)\left(x-5\right)
To find the opposite of 3x^{2}-5x-2, find the opposite of each term.
5x+2-2\left(x+1\right)\left(x-5\right)
Combine 3x^{2} and -3x^{2} to get 0.
5x+2+\left(-2x-2\right)\left(x-5\right)
Use the distributive property to multiply -2 by x+1.
5x+2-2x^{2}+8x+10
Use the distributive property to multiply -2x-2 by x-5 and combine like terms.
13x+2-2x^{2}+10
Combine 5x and 8x to get 13x.
13x+12-2x^{2}
Add 2 and 10 to get 12.
3x^{2}-\left(3x^{2}-5x-2\right)-2\left(x+1\right)\left(x-5\right)
Use the distributive property to multiply x-2 by 3x+1 and combine like terms.
3x^{2}-3x^{2}+5x+2-2\left(x+1\right)\left(x-5\right)
To find the opposite of 3x^{2}-5x-2, find the opposite of each term.
5x+2-2\left(x+1\right)\left(x-5\right)
Combine 3x^{2} and -3x^{2} to get 0.
5x+2+\left(-2x-2\right)\left(x-5\right)
Use the distributive property to multiply -2 by x+1.
5x+2-2x^{2}+8x+10
Use the distributive property to multiply -2x-2 by x-5 and combine like terms.
13x+2-2x^{2}+10
Combine 5x and 8x to get 13x.
13x+12-2x^{2}
Add 2 and 10 to get 12.
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}