Solve 2*(x-10)^2-3*(x-4)=2x^2-4*(x-5)

$$2 \cdot ( x - 10 ) ^ { 2 } - 3 \cdot ( x - 4 ) = 2 x ^ { 2 } - 4 \cdot ( x - 5 )$$

Solve for x

$$x = \frac{64}{13} = 4\frac{12}{13} \approx 4.923076923$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$2\left(x^{2}-20x+100\right)-3\left(x-4\right)=2x^{2}-4\left(x-5\right)$$

Use the distributive property to multiply 2 by x^{2}-20x+100.

$$2x^{2}-40x+200-3\left(x-4\right)=2x^{2}-4\left(x-5\right)$$

Use the distributive property to multiply -3 by x-4.

$$2x^{2}-40x+200-3x+12=2x^{2}-4\left(x-5\right)$$

Combine -40x and -3x to get -43x.

$$2x^{2}-43x+200+12=2x^{2}-4\left(x-5\right)$$

Add 200 and 12 to get 212.

$$2x^{2}-43x+212=2x^{2}-4\left(x-5\right)$$

Use the distributive property to multiply -4 by x-5.

$$2x^{2}-43x+212=2x^{2}-4x+20$$

Subtract 2x^{2} from both sides.

$$2x^{2}-43x+212-2x^{2}=-4x+20$$

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

$$-43x+212=-4x+20$$

Add 4x to both sides.

$$-43x+212+4x=20$$

Combine -43x and 4x to get -39x.

$$-39x+212=20$$

Subtract 212 from both sides.

$$-39x=20-212$$

Subtract 212 from 20 to get -192.

$$-39x=-192$$

Divide both sides by -39.

$$x=\frac{-192}{-39}$$

Reduce the fraction \frac{-192}{-39} to lowest terms by extracting and canceling out -3.

$$x=\frac{64}{13}$$