Solve (2x+3)(4x-3)-17=2x(4x+1)

$$( 2 x + 3 ) ( 4 x - 3 ) - 17 = 2 x ( 4 x + 1 )$$

Solve for x

$$x = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+3 by 4x-3 and combine like terms.

$$8x^{2}+6x-9-17=2x\left(4x+1\right)$$

Subtract 17 from -9 to get -26.

$$8x^{2}+6x-26=2x\left(4x+1\right)$$

Use the distributive property to multiply 2x by 4x+1.

$$8x^{2}+6x-26=8x^{2}+2x$$

Subtract 8x^{2} from both sides.

$$8x^{2}+6x-26-8x^{2}=2x$$

Combine 8x^{2} and -8x^{2} to get 0.

$$6x-26=2x$$

Subtract 2x from both sides.

$$6x-26-2x=0$$

Combine 6x and -2x to get 4x.

$$4x-26=0$$

Add 26 to both sides. Anything plus zero gives itself.

$$4x=26$$

Divide both sides by 4.

$$x=\frac{26}{4}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{13}{2}$$