2(x-2)(x+3)-(2x+4)(x-2)=0

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Solution for 2(x-2)(x+3)-(2x+4)(x-2)=0 equation: 


Simplifying
2(x + -2)(x + 3) + -1(2x + 4)(x + -2) = 0

Reorder the terms:
2(-2 + x)(x + 3) + -1(2x + 4)(x + -2) = 0

Reorder the terms:
2(-2 + x)(3 + x) + -1(2x + 4)(x + -2) = 0

Multiply (-2 + x) * (3 + x)
2(-2(3 + x) + x(3 + x)) + -1(2x + 4)(x + -2) = 0
2((3 * -2 + x * -2) + x(3 + x)) + -1(2x + 4)(x + -2) = 0
2((-6 + -2x) + x(3 + x)) + -1(2x + 4)(x + -2) = 0
2(-6 + -2x + (3 * x + x * x)) + -1(2x + 4)(x + -2) = 0
2(-6 + -2x + (3x + x2)) + -1(2x + 4)(x + -2) = 0

Combine like terms: -2x + 3x = 1x
2(-6 + 1x + x2) + -1(2x + 4)(x + -2) = 0
(-6 * 2 + 1x * 2 + x2 * 2) + -1(2x + 4)(x + -2) = 0
(-12 + 2x + 2x2) + -1(2x + 4)(x + -2) = 0

Reorder the terms:
-12 + 2x + 2x2 + -1(4 + 2x)(x + -2) = 0

Reorder the terms:
-12 + 2x + 2x2 + -1(4 + 2x)(-2 + x) = 0

Multiply (4 + 2x) * (-2 + x)
-12 + 2x + 2x2 + -1(4(-2 + x) + 2x * (-2 + x)) = 0
-12 + 2x + 2x2 + -1((-2 * 4 + x * 4) + 2x * (-2 + x)) = 0
-12 + 2x + 2x2 + -1((-8 + 4x) + 2x * (-2 + x)) = 0
-12 + 2x + 2x2 + -1(-8 + 4x + (-2 * 2x + x * 2x)) = 0
-12 + 2x + 2x2 + -1(-8 + 4x + (-4x + 2x2)) = 0

Combine like terms: 4x + -4x = 0
-12 + 2x + 2x2 + -1(-8 + 0 + 2x2) = 0
-12 + 2x + 2x2 + -1(-8 + 2x2) = 0
-12 + 2x + 2x2 + (-8 * -1 + 2x2 * -1) = 0
-12 + 2x + 2x2 + (8 + -2x2) = 0

Reorder the terms:
-12 + 8 + 2x + 2x2 + -2x2 = 0

Combine like terms: -12 + 8 = -4
-4 + 2x + 2x2 + -2x2 = 0

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

Solving
-4 + 2x = 0

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + 2x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2x = 0 + 4
2x = 0 + 4

Combine like terms: 0 + 4 = 4
2x = 4

Divide each side by '2'.
x = 2

Simplifying
x = 2

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