Solve (2x-1)(1+4x)-5x^2=8+(x-1)(3x+5)

$$( 2 x - 1 ) ( 1 + 4 x ) - 5 x ^ { 2 } = 8 + ( x - 1 ) ( 3 x + 5 )$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by 1+4x and combine like terms.

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

Combine 8x^{2} and -5x^{2} to get 3x^{2}.

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

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

$$-2x+3x^{2}-1=8+3x^{2}+2x-5$$

Subtract 5 from 8 to get 3.

$$-2x+3x^{2}-1=3+3x^{2}+2x$$

Subtract 3x^{2} from both sides.

$$-2x+3x^{2}-1-3x^{2}=3+2x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-2x-1=3+2x$$

Subtract 2x from both sides.

$$-2x-1-2x=3$$

Combine -2x and -2x to get -4x.

$$-4x-1=3$$

Add 1 to both sides.

$$-4x=3+1$$

Add 3 and 1 to get 4.

$$-4x=4$$

Divide both sides by -4.

$$x=\frac{4}{-4}$$

Divide 4 by -4 to get -1.

$$x=-1$$