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

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


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

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

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

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

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

Reorder the terms:
-12 + 2x + 2x2 + -1(4 + 2x)(x + -3) = 0

Reorder the terms:
-12 + 2x + 2x2 + -1(4 + 2x)(-3 + x) = 0

Multiply (4 + 2x) * (-3 + x)
-12 + 2x + 2x2 + -1(4(-3 + x) + 2x * (-3 + x)) = 0
-12 + 2x + 2x2 + -1((-3 * 4 + x * 4) + 2x * (-3 + x)) = 0
-12 + 2x + 2x2 + -1((-12 + 4x) + 2x * (-3 + x)) = 0
-12 + 2x + 2x2 + -1(-12 + 4x + (-3 * 2x + x * 2x)) = 0
-12 + 2x + 2x2 + -1(-12 + 4x + (-6x + 2x2)) = 0

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

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

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

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

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

Solving
4x = 0

Solving for variable 'x'.

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

Divide each side by '4'.
x = 0

Simplifying
x = 0

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