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

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

Solve for x

$$x = \frac{49}{24} = 2\frac{1}{24} \approx 2.041666667$$

Steps for Solving Linear Equation

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

$$4x^{2}-20x+25=\left(x+3\right)\left(4x-8\right)$$

Use the distributive property to multiply x+3 by 4x-8 and combine like terms.

$$4x^{2}-20x+25=4x^{2}+4x-24$$

Subtract 4x^{2} from both sides.

$$4x^{2}-20x+25-4x^{2}=4x-24$$

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

$$-20x+25=4x-24$$

Subtract 4x from both sides.

$$-20x+25-4x=-24$$

Combine -20x and -4x to get -24x.

$$-24x+25=-24$$

Subtract 25 from both sides.

$$-24x=-24-25$$

Subtract 25 from -24 to get -49.

$$-24x=-49$$

Divide both sides by -24.

$$x=\frac{-49}{-24}$$

Fraction \frac{-49}{-24} can be simplified to \frac{49}{24} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{49}{24}$$