Solve (2x-3)^2+(3x+2)^2-11x(x-3)=2(x+6)(x-6)+40x+43

$$( 2 x - 3 ) ^ { 2 } + ( 3 x + 2 ) ^ { 2 } - 11 x ( x - 3 ) = 2 ( x + 6 ) ( x - 6 ) + 40 x + 43$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$4x^{2}-12x+9+\left(3x+2\right)^{2}-11x\left(x-3\right)=2\left(x+6\right)\left(x-6\right)+40x+43$$

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

$$4x^{2}-12x+9+9x^{2}+12x+4-11x\left(x-3\right)=2\left(x+6\right)\left(x-6\right)+40x+43$$

Combine 4x^{2} and 9x^{2} to get 13x^{2}.

$$13x^{2}-12x+9+12x+4-11x\left(x-3\right)=2\left(x+6\right)\left(x-6\right)+40x+43$$

Combine -12x and 12x to get 0.

$$13x^{2}+9+4-11x\left(x-3\right)=2\left(x+6\right)\left(x-6\right)+40x+43$$

Add 9 and 4 to get 13.

$$13x^{2}+13-11x\left(x-3\right)=2\left(x+6\right)\left(x-6\right)+40x+43$$

Use the distributive property to multiply 2 by x+6.

$$13x^{2}+13-11x\left(x-3\right)=\left(2x+12\right)\left(x-6\right)+40x+43$$

Use the distributive property to multiply 2x+12 by x-6 and combine like terms.

$$13x^{2}+13-11x\left(x-3\right)=2x^{2}-72+40x+43$$

Add -72 and 43 to get -29.

$$13x^{2}+13-11x\left(x-3\right)=2x^{2}-29+40x$$

Subtract 2x^{2} from both sides.

$$13x^{2}+13-11x\left(x-3\right)-2x^{2}=-29+40x$$

Subtract 40x from both sides.

$$13x^{2}+13-11x\left(x-3\right)-2x^{2}-40x=-29$$

Use the distributive property to multiply -11x by x-3.

$$13x^{2}+13-11x^{2}+33x-2x^{2}-40x=-29$$

Combine 13x^{2} and -11x^{2} to get 2x^{2}.

$$2x^{2}+13+33x-2x^{2}-40x=-29$$

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

$$13+33x-40x=-29$$

Combine 33x and -40x to get -7x.

$$13-7x=-29$$

Subtract 13 from both sides.

$$-7x=-29-13$$

Subtract 13 from -29 to get -42.

$$-7x=-42$$

Divide both sides by -7.

$$x=\frac{-42}{-7}$$

Divide -42 by -7 to get 6.

$$x=6$$