0=-3(x+1)(x-6)

Solution for 0=-3(x+1)(x-6) equation:

Simplifying
0 = -3(x + 1)(x + -6)

Reorder the terms:
0 = -3(1 + x)(x + -6)

Reorder the terms:
0 = -3(1 + x)(-6 + x)

Multiply (1 + x) * (-6 + x)
0 = -3(1(-6 + x) + x(-6 + x))
0 = -3((-6 * 1 + x * 1) + x(-6 + x))
0 = -3((-6 + 1x) + x(-6 + x))
0 = -3(-6 + 1x + (-6 * x + x * x))
0 = -3(-6 + 1x + (-6x + x2))

Combine like terms: 1x + -6x = -5x
0 = -3(-6 + -5x + x2)
0 = (-6 * -3 + -5x * -3 + x2 * -3)
0 = (18 + 15x + -3x2)

Solving
0 = 18 + 15x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + -18 = -18
-18 + -15x + 3x2 = 18 + 15x + -3x2 + -18 + -15x + 3x2

Reorder the terms:
-18 + -15x + 3x2 = 18 + -18 + 15x + -15x + -3x2 + 3x2

Combine like terms: 18 + -18 = 0
-18 + -15x + 3x2 = 0 + 15x + -15x + -3x2 + 3x2
-18 + -15x + 3x2 = 15x + -15x + -3x2 + 3x2

Combine like terms: 15x + -15x = 0
-18 + -15x + 3x2 = 0 + -3x2 + 3x2
-18 + -15x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-18 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -5x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(6 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}