(x+6)(x+2)(x-7)(x-3)=180

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Solution for (x+6)(x+2)(x-7)(x-3)=180 equation: 


Simplifying
(x + 6)(x + 2)(x + -7)(x + -3) = 180

Reorder the terms:
(6 + x)(x + 2)(x + -7)(x + -3) = 180

Reorder the terms:
(6 + x)(2 + x)(x + -7)(x + -3) = 180

Reorder the terms:
(6 + x)(2 + x)(-7 + x)(x + -3) = 180

Reorder the terms:
(6 + x)(2 + x)(-7 + x)(-3 + x) = 180

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

Combine like terms: 6x + 2x = 8x
(12 + 8x + x2)(-7 + x)(-3 + x) = 180

Multiply (12 + 8x + x2) * (-7 + x)
(12(-7 + x) + 8x * (-7 + x) + x2(-7 + x))(-3 + x) = 180
((-7 * 12 + x * 12) + 8x * (-7 + x) + x2(-7 + x))(-3 + x) = 180
((-84 + 12x) + 8x * (-7 + x) + x2(-7 + x))(-3 + x) = 180
(-84 + 12x + (-7 * 8x + x * 8x) + x2(-7 + x))(-3 + x) = 180
(-84 + 12x + (-56x + 8x2) + x2(-7 + x))(-3 + x) = 180
(-84 + 12x + -56x + 8x2 + (-7 * x2 + x * x2))(-3 + x) = 180
(-84 + 12x + -56x + 8x2 + (-7x2 + x3))(-3 + x) = 180

Combine like terms: 12x + -56x = -44x
(-84 + -44x + 8x2 + -7x2 + x3)(-3 + x) = 180

Combine like terms: 8x2 + -7x2 = 1x2
(-84 + -44x + 1x2 + x3)(-3 + x) = 180

Multiply (-84 + -44x + 1x2 + x3) * (-3 + x)
(-84(-3 + x) + -44x * (-3 + x) + 1x2 * (-3 + x) + x3(-3 + x)) = 180
((-3 * -84 + x * -84) + -44x * (-3 + x) + 1x2 * (-3 + x) + x3(-3 + x)) = 180
((252 + -84x) + -44x * (-3 + x) + 1x2 * (-3 + x) + x3(-3 + x)) = 180
(252 + -84x + (-3 * -44x + x * -44x) + 1x2 * (-3 + x) + x3(-3 + x)) = 180
(252 + -84x + (132x + -44x2) + 1x2 * (-3 + x) + x3(-3 + x)) = 180
(252 + -84x + 132x + -44x2 + (-3 * 1x2 + x * 1x2) + x3(-3 + x)) = 180
(252 + -84x + 132x + -44x2 + (-3x2 + 1x3) + x3(-3 + x)) = 180
(252 + -84x + 132x + -44x2 + -3x2 + 1x3 + (-3 * x3 + x * x3)) = 180
(252 + -84x + 132x + -44x2 + -3x2 + 1x3 + (-3x3 + x4)) = 180

Combine like terms: -84x + 132x = 48x
(252 + 48x + -44x2 + -3x2 + 1x3 + -3x3 + x4) = 180

Combine like terms: -44x2 + -3x2 = -47x2
(252 + 48x + -47x2 + 1x3 + -3x3 + x4) = 180

Combine like terms: 1x3 + -3x3 = -2x3
(252 + 48x + -47x2 + -2x3 + x4) = 180

Solving
252 + 48x + -47x2 + -2x3 + x4 = 180

Solving for variable 'x'.

Reorder the terms:
252 + -180 + 48x + -47x2 + -2x3 + x4 = 180 + -180

Combine like terms: 252 + -180 = 72
72 + 48x + -47x2 + -2x3 + x4 = 180 + -180

Combine like terms: 180 + -180 = 0
72 + 48x + -47x2 + -2x3 + x4 = 0

The solution to this equation could not be determined.

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