Solve 4x^2-4left(x-2right)x>0

$$4 { x }^{ 2 } -4 \left( x-2 \right) x > 0$$

Solve for x

$$x>0$$

Solution Steps

Multiply -1 and 4 to get -4.

$$4x^{2}-4\left(x-2\right)x>0$$

Use the distributive property to multiply -4 by x-2.

$$4x^{2}+\left(-4x+8\right)x>0$$

Use the distributive property to multiply -4x+8 by x.

$$4x^{2}-4x^{2}+8x>0$$

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

$$8x>0$$

Product of two numbers is >0 if both are >0 or both are <0. Since 8>0, x must be >0.

$$x>0$$