Solve for x
x=-5
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2=x\left(x+3\right)+\left(x+4\right)\left(3-x\right)
Variable x cannot be equal to any of the values -4,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+4\right), the least common multiple of x^{2}+4x,x+4,x.
2=x^{2}+3x+\left(x+4\right)\left(3-x\right)
Use the distributive property to multiply x by x+3.
2=x^{2}+3x-x-x^{2}+12
Use the distributive property to multiply x+4 by 3-x and combine like terms.
2=x^{2}+2x-x^{2}+12
Combine 3x and -x to get 2x.
2=2x+12
Combine x^{2} and -x^{2} to get 0.
2x+12=2
Swap sides so that all variable terms are on the left hand side.
2x=2-12
Subtract 12 from both sides.
2x=-10
Subtract 12 from 2 to get -10.
x=\frac{-10}{2}
Divide both sides by 2.
x=-5
Divide -10 by 2 to get -5.
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
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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}