Solve left(3x+2right)^2-left(2x-1right)^2=-5x(1-x)-18

$${ \left(3x+2 \right) }^{ 2 } - { \left(2x-1 \right) }^{ 2 } =-5x(1-x)-18$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2\right)^{2}.

$$9x^{2}+12x+4-\left(2x-1\right)^{2}=-5x\left(1-x\right)-18$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

$$9x^{2}+12x+4-\left(4x^{2}-4x+1\right)=-5x\left(1-x\right)-18$$

To find the opposite of 4x^{2}-4x+1, find the opposite of each term.

$$9x^{2}+12x+4-4x^{2}+4x-1=-5x\left(1-x\right)-18$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+12x+4+4x-1=-5x\left(1-x\right)-18$$

Combine 12x and 4x to get 16x.

$$5x^{2}+16x+4-1=-5x\left(1-x\right)-18$$

Subtract 1 from 4 to get 3.

$$5x^{2}+16x+3=-5x\left(1-x\right)-18$$

Use the distributive property to multiply -5x by 1-x.

$$5x^{2}+16x+3=-5x+5x^{2}-18$$

Add 5x to both sides.

$$5x^{2}+16x+3+5x=5x^{2}-18$$

Combine 16x and 5x to get 21x.

$$5x^{2}+21x+3=5x^{2}-18$$

Subtract 5x^{2} from both sides.

$$5x^{2}+21x+3-5x^{2}=-18$$

Combine 5x^{2} and -5x^{2} to get 0.

$$21x+3=-18$$

Subtract 3 from both sides.

$$21x=-18-3$$

Subtract 3 from -18 to get -21.

$$21x=-21$$

Divide both sides by 21.

$$x=\frac{-21}{21}$$

Divide -21 by 21 to get -1.

$$x=-1$$