Solve 3x(3x-2)-87=8x(x-2)+(x+1)^2

$$3 x ( 3 x - 2 ) - 87 = 8 x ( x - 2 ) + ( x + 1 ) ^ { 2 }$$

Solve for x

$$x=11$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 3x-2.

$$9x^{2}-6x-87=8x\left(x-2\right)+\left(x+1\right)^{2}$$

Use the distributive property to multiply 8x by x-2.

$$9x^{2}-6x-87=8x^{2}-16x+\left(x+1\right)^{2}$$

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

$$9x^{2}-6x-87=8x^{2}-16x+x^{2}+2x+1$$

Combine 8x^{2} and x^{2} to get 9x^{2}.

$$9x^{2}-6x-87=9x^{2}-16x+2x+1$$

Combine -16x and 2x to get -14x.

$$9x^{2}-6x-87=9x^{2}-14x+1$$

Subtract 9x^{2} from both sides.

$$9x^{2}-6x-87-9x^{2}=-14x+1$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-6x-87=-14x+1$$

Add 14x to both sides.

$$-6x-87+14x=1$$

Combine -6x and 14x to get 8x.

$$8x-87=1$$

Add 87 to both sides.

$$8x=1+87$$

Add 1 and 87 to get 88.

$$8x=88$$

Divide both sides by 8.

$$x=\frac{88}{8}$$

Divide 88 by 8 to get 11.

$$x=11$$