Solve (2x-7)(x+1)+3(4x-1)(4x+1)=2(5x-2)^2-53

$$( 2 x - 7 ) ( x + 1 ) + 3 ( 4 x - 1 ) ( 4 x + 1 ) = 2 ( 5 x - 2 ) ^ { 2 } - 53$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-7 by x+1 and combine like terms.

$$2x^{2}-5x-7+3\left(4x-1\right)\left(4x+1\right)=2\left(5x-2\right)^{2}-53$$

Use the distributive property to multiply 3 by 4x-1.

$$2x^{2}-5x-7+\left(12x-3\right)\left(4x+1\right)=2\left(5x-2\right)^{2}-53$$

Use the distributive property to multiply 12x-3 by 4x+1 and combine like terms.

$$2x^{2}-5x-7+48x^{2}-3=2\left(5x-2\right)^{2}-53$$

Combine 2x^{2} and 48x^{2} to get 50x^{2}.

$$50x^{2}-5x-7-3=2\left(5x-2\right)^{2}-53$$

Subtract 3 from -7 to get -10.

$$50x^{2}-5x-10=2\left(5x-2\right)^{2}-53$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5x-2\right)^{2}.

$$50x^{2}-5x-10=2\left(25x^{2}-20x+4\right)-53$$

Use the distributive property to multiply 2 by 25x^{2}-20x+4.

$$50x^{2}-5x-10=50x^{2}-40x+8-53$$

Subtract 53 from 8 to get -45.

$$50x^{2}-5x-10=50x^{2}-40x-45$$

Subtract 50x^{2} from both sides.

$$50x^{2}-5x-10-50x^{2}=-40x-45$$

Combine 50x^{2} and -50x^{2} to get 0.

$$-5x-10=-40x-45$$

Add 40x to both sides.

$$-5x-10+40x=-45$$

Combine -5x and 40x to get 35x.

$$35x-10=-45$$

Add 10 to both sides.

$$35x=-45+10$$

Add -45 and 10 to get -35.

$$35x=-35$$

Divide both sides by 35.

$$x=\frac{-35}{35}$$

Divide -35 by 35 to get -1.

$$x=-1$$