(x+2)(x+3)(x-4)(x-6)=10x^2

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Solution for (x+2)(x+3)(x-4)(x-6)=10x^2 equation: 


Simplifying
(x + 2)(x + 3)(x + -4)(x + -6) = 10x2

Reorder the terms:
(2 + x)(x + 3)(x + -4)(x + -6) = 10x2

Reorder the terms:
(2 + x)(3 + x)(x + -4)(x + -6) = 10x2

Reorder the terms:
(2 + x)(3 + x)(-4 + x)(x + -6) = 10x2

Reorder the terms:
(2 + x)(3 + x)(-4 + x)(-6 + x) = 10x2

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x))(-4 + x)(-6 + x) = 10x2
((3 * 2 + x * 2) + x(3 + x))(-4 + x)(-6 + x) = 10x2
((6 + 2x) + x(3 + x))(-4 + x)(-6 + x) = 10x2
(6 + 2x + (3 * x + x * x))(-4 + x)(-6 + x) = 10x2
(6 + 2x + (3x + x2))(-4 + x)(-6 + x) = 10x2

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2)(-4 + x)(-6 + x) = 10x2

Multiply (6 + 5x + x2) * (-4 + x)
(6(-4 + x) + 5x * (-4 + x) + x2(-4 + x))(-6 + x) = 10x2
((-4 * 6 + x * 6) + 5x * (-4 + x) + x2(-4 + x))(-6 + x) = 10x2
((-24 + 6x) + 5x * (-4 + x) + x2(-4 + x))(-6 + x) = 10x2
(-24 + 6x + (-4 * 5x + x * 5x) + x2(-4 + x))(-6 + x) = 10x2
(-24 + 6x + (-20x + 5x2) + x2(-4 + x))(-6 + x) = 10x2
(-24 + 6x + -20x + 5x2 + (-4 * x2 + x * x2))(-6 + x) = 10x2
(-24 + 6x + -20x + 5x2 + (-4x2 + x3))(-6 + x) = 10x2

Combine like terms: 6x + -20x = -14x
(-24 + -14x + 5x2 + -4x2 + x3)(-6 + x) = 10x2

Combine like terms: 5x2 + -4x2 = 1x2
(-24 + -14x + 1x2 + x3)(-6 + x) = 10x2

Multiply (-24 + -14x + 1x2 + x3) * (-6 + x)
(-24(-6 + x) + -14x * (-6 + x) + 1x2 * (-6 + x) + x3(-6 + x)) = 10x2
((-6 * -24 + x * -24) + -14x * (-6 + x) + 1x2 * (-6 + x) + x3(-6 + x)) = 10x2
((144 + -24x) + -14x * (-6 + x) + 1x2 * (-6 + x) + x3(-6 + x)) = 10x2
(144 + -24x + (-6 * -14x + x * -14x) + 1x2 * (-6 + x) + x3(-6 + x)) = 10x2
(144 + -24x + (84x + -14x2) + 1x2 * (-6 + x) + x3(-6 + x)) = 10x2
(144 + -24x + 84x + -14x2 + (-6 * 1x2 + x * 1x2) + x3(-6 + x)) = 10x2
(144 + -24x + 84x + -14x2 + (-6x2 + 1x3) + x3(-6 + x)) = 10x2
(144 + -24x + 84x + -14x2 + -6x2 + 1x3 + (-6 * x3 + x * x3)) = 10x2
(144 + -24x + 84x + -14x2 + -6x2 + 1x3 + (-6x3 + x4)) = 10x2

Combine like terms: -24x + 84x = 60x
(144 + 60x + -14x2 + -6x2 + 1x3 + -6x3 + x4) = 10x2

Combine like terms: -14x2 + -6x2 = -20x2
(144 + 60x + -20x2 + 1x3 + -6x3 + x4) = 10x2

Combine like terms: 1x3 + -6x3 = -5x3
(144 + 60x + -20x2 + -5x3 + x4) = 10x2

Solving
144 + 60x + -20x2 + -5x3 + x4 = 10x2

Solving for variable 'x'.

Reorder the terms:
144 + 60x + -20x2 + -10x2 + -5x3 + x4 = 10x2 + -10x2

Combine like terms: -20x2 + -10x2 = -30x2
144 + 60x + -30x2 + -5x3 + x4 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
144 + 60x + -30x2 + -5x3 + x4 = 0

The solution to this equation could not be determined.

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