3(x+6)(x-2)=60

Solution for 3(x+6)(x-2)=60 equation:

Simplifying
3(x + 6)(x + -2) = 60

Reorder the terms:
3(6 + x)(x + -2) = 60

Reorder the terms:
3(6 + x)(-2 + x) = 60

Multiply (6 + x) * (-2 + x)
3(6(-2 + x) + x(-2 + x)) = 60
3((-2 * 6 + x * 6) + x(-2 + x)) = 60
3((-12 + 6x) + x(-2 + x)) = 60
3(-12 + 6x + (-2 * x + x * x)) = 60
3(-12 + 6x + (-2x + x2)) = 60

Combine like terms: 6x + -2x = 4x
3(-12 + 4x + x2) = 60
(-12 * 3 + 4x * 3 + x2 * 3) = 60
(-36 + 12x + 3x2) = 60

Solving
-36 + 12x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
-36 + -60 + 12x + 3x2 = 60 + -60

Combine like terms: -36 + -60 = -96
-96 + 12x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-96 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + 4x + x2) = 0

Factor a trinomial.
3((-8 + -1x)(4 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8, 4}