2(3x-2)(x-4)-7(x-6)(x+2)=0

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Solution for 2(3x-2)(x-4)-7(x-6)(x+2)=0 equation: 


Simplifying
2(3x + -2)(x + -4) + -7(x + -6)(x + 2) = 0

Reorder the terms:
2(-2 + 3x)(x + -4) + -7(x + -6)(x + 2) = 0

Reorder the terms:
2(-2 + 3x)(-4 + x) + -7(x + -6)(x + 2) = 0

Multiply (-2 + 3x) * (-4 + x)
2(-2(-4 + x) + 3x * (-4 + x)) + -7(x + -6)(x + 2) = 0
2((-4 * -2 + x * -2) + 3x * (-4 + x)) + -7(x + -6)(x + 2) = 0
2((8 + -2x) + 3x * (-4 + x)) + -7(x + -6)(x + 2) = 0
2(8 + -2x + (-4 * 3x + x * 3x)) + -7(x + -6)(x + 2) = 0
2(8 + -2x + (-12x + 3x2)) + -7(x + -6)(x + 2) = 0

Combine like terms: -2x + -12x = -14x
2(8 + -14x + 3x2) + -7(x + -6)(x + 2) = 0
(8 * 2 + -14x * 2 + 3x2 * 2) + -7(x + -6)(x + 2) = 0
(16 + -28x + 6x2) + -7(x + -6)(x + 2) = 0

Reorder the terms:
16 + -28x + 6x2 + -7(-6 + x)(x + 2) = 0

Reorder the terms:
16 + -28x + 6x2 + -7(-6 + x)(2 + x) = 0

Multiply (-6 + x) * (2 + x)
16 + -28x + 6x2 + -7(-6(2 + x) + x(2 + x)) = 0
16 + -28x + 6x2 + -7((2 * -6 + x * -6) + x(2 + x)) = 0
16 + -28x + 6x2 + -7((-12 + -6x) + x(2 + x)) = 0
16 + -28x + 6x2 + -7(-12 + -6x + (2 * x + x * x)) = 0
16 + -28x + 6x2 + -7(-12 + -6x + (2x + x2)) = 0

Combine like terms: -6x + 2x = -4x
16 + -28x + 6x2 + -7(-12 + -4x + x2) = 0
16 + -28x + 6x2 + (-12 * -7 + -4x * -7 + x2 * -7) = 0
16 + -28x + 6x2 + (84 + 28x + -7x2) = 0

Reorder the terms:
16 + 84 + -28x + 28x + 6x2 + -7x2 = 0

Combine like terms: 16 + 84 = 100
100 + -28x + 28x + 6x2 + -7x2 = 0

Combine like terms: -28x + 28x = 0
100 + 0 + 6x2 + -7x2 = 0
100 + 6x2 + -7x2 = 0

Combine like terms: 6x2 + -7x2 = -1x2
100 + -1x2 = 0

Solving
100 + -1x2 = 0

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + -1x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x2 = 0 + -100
-1x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-1x2 = -100

Divide each side by '-1'.
x2 = 100

Simplifying
x2 = 100

Take the square root of each side:
x = {-10, 10}

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