2x-4x+4=(3x+4)(x-2)

Solution for 2x-4x+4=(3x+4)(x-2) equation:

Simplifying
2x + -4x + 4 = (3x + 4)(x + -2)

Reorder the terms:
4 + 2x + -4x = (3x + 4)(x + -2)

Combine like terms: 2x + -4x = -2x
4 + -2x = (3x + 4)(x + -2)

Reorder the terms:
4 + -2x = (4 + 3x)(x + -2)

Reorder the terms:
4 + -2x = (4 + 3x)(-2 + x)

Multiply (4 + 3x) * (-2 + x)
4 + -2x = (4(-2 + x) + 3x * (-2 + x))
4 + -2x = ((-2 * 4 + x * 4) + 3x * (-2 + x))
4 + -2x = ((-8 + 4x) + 3x * (-2 + x))
4 + -2x = (-8 + 4x + (-2 * 3x + x * 3x))
4 + -2x = (-8 + 4x + (-6x + 3x2))

Combine like terms: 4x + -6x = -2x
4 + -2x = (-8 + -2x + 3x2)

Add '2x' to each side of the equation.
4 + -2x + 2x = -8 + -2x + 2x + 3x2

Combine like terms: -2x + 2x = 0
4 + 0 = -8 + -2x + 2x + 3x2
4 = -8 + -2x + 2x + 3x2

Combine like terms: -2x + 2x = 0
4 = -8 + 0 + 3x2
4 = -8 + 3x2

Solving
4 = -8 + 3x2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x2' to each side of the equation.
4 + -3x2 = -8 + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + -3x2 = -8 + 0
4 + -3x2 = -8

Add '-4' to each side of the equation.
4 + -4 + -3x2 = -8 + -4

Combine like terms: 4 + -4 = 0
0 + -3x2 = -8 + -4
-3x2 = -8 + -4

Combine like terms: -8 + -4 = -12
-3x2 = -12

Divide each side by '-3'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}