(x+2)(x+3)(x-5)(x-6)=180

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Solution for (x+2)(x+3)(x-5)(x-6)=180 equation: 


Simplifying
(x + 2)(x + 3)(x + -5)(x + -6) = 180

Reorder the terms:
(2 + x)(x + 3)(x + -5)(x + -6) = 180

Reorder the terms:
(2 + x)(3 + x)(x + -5)(x + -6) = 180

Reorder the terms:
(2 + x)(3 + x)(-5 + x)(x + -6) = 180

Reorder the terms:
(2 + x)(3 + x)(-5 + x)(-6 + x) = 180

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x))(-5 + x)(-6 + x) = 180
((3 * 2 + x * 2) + x(3 + x))(-5 + x)(-6 + x) = 180
((6 + 2x) + x(3 + x))(-5 + x)(-6 + x) = 180
(6 + 2x + (3 * x + x * x))(-5 + x)(-6 + x) = 180
(6 + 2x + (3x + x2))(-5 + x)(-6 + x) = 180

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2)(-5 + x)(-6 + x) = 180

Multiply (6 + 5x + x2) * (-5 + x)
(6(-5 + x) + 5x * (-5 + x) + x2(-5 + x))(-6 + x) = 180
((-5 * 6 + x * 6) + 5x * (-5 + x) + x2(-5 + x))(-6 + x) = 180
((-30 + 6x) + 5x * (-5 + x) + x2(-5 + x))(-6 + x) = 180
(-30 + 6x + (-5 * 5x + x * 5x) + x2(-5 + x))(-6 + x) = 180
(-30 + 6x + (-25x + 5x2) + x2(-5 + x))(-6 + x) = 180
(-30 + 6x + -25x + 5x2 + (-5 * x2 + x * x2))(-6 + x) = 180
(-30 + 6x + -25x + 5x2 + (-5x2 + x3))(-6 + x) = 180

Combine like terms: 6x + -25x = -19x
(-30 + -19x + 5x2 + -5x2 + x3)(-6 + x) = 180

Combine like terms: 5x2 + -5x2 = 0
(-30 + -19x + 0 + x3)(-6 + x) = 180
(-30 + -19x + x3)(-6 + x) = 180

Multiply (-30 + -19x + x3) * (-6 + x)
(-30(-6 + x) + -19x * (-6 + x) + x3(-6 + x)) = 180
((-6 * -30 + x * -30) + -19x * (-6 + x) + x3(-6 + x)) = 180
((180 + -30x) + -19x * (-6 + x) + x3(-6 + x)) = 180
(180 + -30x + (-6 * -19x + x * -19x) + x3(-6 + x)) = 180
(180 + -30x + (114x + -19x2) + x3(-6 + x)) = 180
(180 + -30x + 114x + -19x2 + (-6 * x3 + x * x3)) = 180
(180 + -30x + 114x + -19x2 + (-6x3 + x4)) = 180

Combine like terms: -30x + 114x = 84x
(180 + 84x + -19x2 + -6x3 + x4) = 180

Add '-180' to each side of the equation.
180 + 84x + -19x2 + -6x3 + -180 + x4 = 180 + -180

Reorder the terms:
180 + -180 + 84x + -19x2 + -6x3 + x4 = 180 + -180

Combine like terms: 180 + -180 = 0
0 + 84x + -19x2 + -6x3 + x4 = 180 + -180
84x + -19x2 + -6x3 + x4 = 180 + -180

Combine like terms: 180 + -180 = 0
84x + -19x2 + -6x3 + x4 = 0

Solving
84x + -19x2 + -6x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(84 + -19x + -6x2 + x3) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(84 + -19x + -6x2 + x3)' equal to zero and attempt to solve:

Simplifying
84 + -19x + -6x2 + x3 = 0

Solving
84 + -19x + -6x2 + x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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