0=-6(x^2-6x-7)

Solution for 0=-6(x^2-6x-7) equation:

Simplifying
0 = -6(x2 + -6x + -7)

Reorder the terms:
0 = -6(-7 + -6x + x2)
0 = (-7 * -6 + -6x * -6 + x2 * -6)
0 = (42 + 36x + -6x2)

Solving
0 = 42 + 36x + -6x2

Solving for variable 'x'.

Combine like terms: 0 + -42 = -42
-42 + -36x + 6x2 = 42 + 36x + -6x2 + -42 + -36x + 6x2

Reorder the terms:
-42 + -36x + 6x2 = 42 + -42 + 36x + -36x + -6x2 + 6x2

Combine like terms: 42 + -42 = 0
-42 + -36x + 6x2 = 0 + 36x + -36x + -6x2 + 6x2
-42 + -36x + 6x2 = 36x + -36x + -6x2 + 6x2

Combine like terms: 36x + -36x = 0
-42 + -36x + 6x2 = 0 + -6x2 + 6x2
-42 + -36x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-42 + -36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -6x + x2) = 0

Factor a trinomial.
6((-1 + -1x)(7 + -1x)) = 0

Ignore the factor 6.
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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}