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

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

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

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

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

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

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

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

Combine like terms: -3x + -2x = -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}