Solve (x+1)(x-2)-(4x-1)(3x+5)-6=8x-11(x-3)(x+7)

$$( x + 1 ) ( x - 2 ) - ( 4 x - 1 ) ( 3 x + 5 ) - 6 = 8 x - 11 ( x - 3 ) ( x + 7 )$$

Solve for x

$$x=13$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x-2 and combine like terms.

$$x^{2}-x-2-\left(4x-1\right)\left(3x+5\right)-6=8x-11\left(x-3\right)\left(x+7\right)$$

Use the distributive property to multiply 4x-1 by 3x+5 and combine like terms.

$$x^{2}-x-2-\left(12x^{2}+17x-5\right)-6=8x-11\left(x-3\right)\left(x+7\right)$$

To find the opposite of 12x^{2}+17x-5, find the opposite of each term.

$$x^{2}-x-2-12x^{2}-17x+5-6=8x-11\left(x-3\right)\left(x+7\right)$$

Combine x^{2} and -12x^{2} to get -11x^{2}.

$$-11x^{2}-x-2-17x+5-6=8x-11\left(x-3\right)\left(x+7\right)$$

Combine -x and -17x to get -18x.

$$-11x^{2}-18x-2+5-6=8x-11\left(x-3\right)\left(x+7\right)$$

Add -2 and 5 to get 3.

$$-11x^{2}-18x+3-6=8x-11\left(x-3\right)\left(x+7\right)$$

Subtract 6 from 3 to get -3.

$$-11x^{2}-18x-3=8x-11\left(x-3\right)\left(x+7\right)$$

Add 11\left(x-3\right)\left(x+7\right) to both sides.

$$-11x^{2}-18x-3+11\left(x-3\right)\left(x+7\right)=8x$$

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

$$-11x^{2}-18x-3+\left(11x-33\right)\left(x+7\right)=8x$$

Use the distributive property to multiply 11x-33 by x+7 and combine like terms.

$$-11x^{2}-18x-3+11x^{2}+44x-231=8x$$

Combine -11x^{2} and 11x^{2} to get 0.

$$-18x-3+44x-231=8x$$

Combine -18x and 44x to get 26x.

$$26x-3-231=8x$$

Subtract 231 from -3 to get -234.

$$26x-234=8x$$

Subtract 8x from both sides.

$$26x-234-8x=0$$

Combine 26x and -8x to get 18x.

$$18x-234=0$$

Add 234 to both sides. Anything plus zero gives itself.

$$18x=234$$

Divide both sides by 18.

$$x=\frac{234}{18}$$

Divide 234 by 18 to get 13.

$$x=13$$