(x+1)(x+2)(x-6)(x-7)=180

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Solution for (x+1)(x+2)(x-6)(x-7)=180 equation: 


Simplifying
(x + 1)(x + 2)(x + -6)(x + -7) = 180

Reorder the terms:
(1 + x)(x + 2)(x + -6)(x + -7) = 180

Reorder the terms:
(1 + x)(2 + x)(x + -6)(x + -7) = 180

Reorder the terms:
(1 + x)(2 + x)(-6 + x)(x + -7) = 180

Reorder the terms:
(1 + x)(2 + x)(-6 + x)(-7 + x) = 180

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x))(-6 + x)(-7 + x) = 180
((2 * 1 + x * 1) + x(2 + x))(-6 + x)(-7 + x) = 180
((2 + 1x) + x(2 + x))(-6 + x)(-7 + x) = 180
(2 + 1x + (2 * x + x * x))(-6 + x)(-7 + x) = 180
(2 + 1x + (2x + x2))(-6 + x)(-7 + x) = 180

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2)(-6 + x)(-7 + x) = 180

Multiply (2 + 3x + x2) * (-6 + x)
(2(-6 + x) + 3x * (-6 + x) + x2(-6 + x))(-7 + x) = 180
((-6 * 2 + x * 2) + 3x * (-6 + x) + x2(-6 + x))(-7 + x) = 180
((-12 + 2x) + 3x * (-6 + x) + x2(-6 + x))(-7 + x) = 180
(-12 + 2x + (-6 * 3x + x * 3x) + x2(-6 + x))(-7 + x) = 180
(-12 + 2x + (-18x + 3x2) + x2(-6 + x))(-7 + x) = 180
(-12 + 2x + -18x + 3x2 + (-6 * x2 + x * x2))(-7 + x) = 180
(-12 + 2x + -18x + 3x2 + (-6x2 + x3))(-7 + x) = 180

Combine like terms: 2x + -18x = -16x
(-12 + -16x + 3x2 + -6x2 + x3)(-7 + x) = 180

Combine like terms: 3x2 + -6x2 = -3x2
(-12 + -16x + -3x2 + x3)(-7 + x) = 180

Multiply (-12 + -16x + -3x2 + x3) * (-7 + x)
(-12(-7 + x) + -16x * (-7 + x) + -3x2 * (-7 + x) + x3(-7 + x)) = 180
((-7 * -12 + x * -12) + -16x * (-7 + x) + -3x2 * (-7 + x) + x3(-7 + x)) = 180
((84 + -12x) + -16x * (-7 + x) + -3x2 * (-7 + x) + x3(-7 + x)) = 180
(84 + -12x + (-7 * -16x + x * -16x) + -3x2 * (-7 + x) + x3(-7 + x)) = 180
(84 + -12x + (112x + -16x2) + -3x2 * (-7 + x) + x3(-7 + x)) = 180
(84 + -12x + 112x + -16x2 + (-7 * -3x2 + x * -3x2) + x3(-7 + x)) = 180
(84 + -12x + 112x + -16x2 + (21x2 + -3x3) + x3(-7 + x)) = 180
(84 + -12x + 112x + -16x2 + 21x2 + -3x3 + (-7 * x3 + x * x3)) = 180
(84 + -12x + 112x + -16x2 + 21x2 + -3x3 + (-7x3 + x4)) = 180

Combine like terms: -12x + 112x = 100x
(84 + 100x + -16x2 + 21x2 + -3x3 + -7x3 + x4) = 180

Combine like terms: -16x2 + 21x2 = 5x2
(84 + 100x + 5x2 + -3x3 + -7x3 + x4) = 180

Combine like terms: -3x3 + -7x3 = -10x3
(84 + 100x + 5x2 + -10x3 + x4) = 180

Solving
84 + 100x + 5x2 + -10x3 + x4 = 180

Solving for variable 'x'.

Reorder the terms:
84 + -180 + 100x + 5x2 + -10x3 + x4 = 180 + -180

Combine like terms: 84 + -180 = -96
-96 + 100x + 5x2 + -10x3 + x4 = 180 + -180

Combine like terms: 180 + -180 = 0
-96 + 100x + 5x2 + -10x3 + x4 = 0

The solution to this equation could not be determined.

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