Solve (7x+1)(x-3)+20(x-1)(x+1)=3(3x-2)^2+13

$$( 7 x + 1 ) ( x - 3 ) + 20 ( x - 1 ) ( x + 1 ) = 3 ( 3 x - 2 ) ^ { 2 } + 13$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7x+1 by x-3 and combine like terms.

$$7x^{2}-20x-3+20\left(x-1\right)\left(x+1\right)=3\left(3x-2\right)^{2}+13$$

Use the distributive property to multiply 20 by x-1.

$$7x^{2}-20x-3+\left(20x-20\right)\left(x+1\right)=3\left(3x-2\right)^{2}+13$$

Use the distributive property to multiply 20x-20 by x+1 and combine like terms.

$$7x^{2}-20x-3+20x^{2}-20=3\left(3x-2\right)^{2}+13$$

Combine 7x^{2} and 20x^{2} to get 27x^{2}.

$$27x^{2}-20x-3-20=3\left(3x-2\right)^{2}+13$$

Subtract 20 from -3 to get -23.

$$27x^{2}-20x-23=3\left(3x-2\right)^{2}+13$$

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

$$27x^{2}-20x-23=3\left(9x^{2}-12x+4\right)+13$$

Use the distributive property to multiply 3 by 9x^{2}-12x+4.

$$27x^{2}-20x-23=27x^{2}-36x+12+13$$

Add 12 and 13 to get 25.

$$27x^{2}-20x-23=27x^{2}-36x+25$$

Subtract 27x^{2} from both sides.

$$27x^{2}-20x-23-27x^{2}=-36x+25$$

Combine 27x^{2} and -27x^{2} to get 0.

$$-20x-23=-36x+25$$

Add 36x to both sides.

$$-20x-23+36x=25$$

Combine -20x and 36x to get 16x.

$$16x-23=25$$

Add 23 to both sides.

$$16x=25+23$$

Add 25 and 23 to get 48.

$$16x=48$$

Divide both sides by 16.

$$x=\frac{48}{16}$$

Divide 48 by 16 to get 3.

$$x=3$$