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

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

Solve for x

$$x = -\frac{55}{8} = -6\frac{7}{8} = -6.875$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 4x-4 by x+2 and combine like terms.

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

Use the distributive property to multiply -5 by x+7.

$$4x^{2}+4x-8-5x-35=\left(2x+3\right)^{2}-5x+3$$

Combine 4x and -5x to get -x.

$$4x^{2}-x-8-35=\left(2x+3\right)^{2}-5x+3$$

Subtract 35 from -8 to get -43.

$$4x^{2}-x-43=\left(2x+3\right)^{2}-5x+3$$

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

$$4x^{2}-x-43=4x^{2}+12x+9-5x+3$$

Combine 12x and -5x to get 7x.

$$4x^{2}-x-43=4x^{2}+7x+9+3$$

Add 9 and 3 to get 12.

$$4x^{2}-x-43=4x^{2}+7x+12$$

Subtract 4x^{2} from both sides.

$$4x^{2}-x-43-4x^{2}=7x+12$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-x-43=7x+12$$

Subtract 7x from both sides.

$$-x-43-7x=12$$

Combine -x and -7x to get -8x.

$$-8x-43=12$$

Add 43 to both sides.

$$-8x=12+43$$

Add 12 and 43 to get 55.

$$-8x=55$$

Divide both sides by -8.

$$x=\frac{55}{-8}$$

Fraction \frac{55}{-8} can be rewritten as -\frac{55}{8} by extracting the negative sign.

$$x=-\frac{55}{8}$$