Solve (2x+3)^2-6x-4=2x(1+2x)

$$( 2 x + 3 ) ^ { 2 } - 6 x - 4 = 2 x ( 1 + 2 x )$$

Solve for x

$$x = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps for Solving Linear Equation

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

$$4x^{2}+12x+9-6x-4=2x\left(1+2x\right)$$

Combine 12x and -6x to get 6x.

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

Subtract 4 from 9 to get 5.

$$4x^{2}+6x+5=2x\left(1+2x\right)$$

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

$$4x^{2}+6x+5=2x+4x^{2}$$

Subtract 2x from both sides.

$$4x^{2}+6x+5-2x=4x^{2}$$

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

$$4x^{2}+4x+5=4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}+4x+5-4x^{2}=0$$

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

$$4x+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$4x=-5$$

Divide both sides by 4.

$$x=\frac{-5}{4}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$x=-\frac{5}{4}$$