(7x-7)(x+6)=

Solution for (7x-7)(x+6)= equation:

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

Reorder the terms:
(-7 + 7x)(x + 6) = 0

Reorder the terms:
(-7 + 7x)(6 + x) = 0

Multiply (-7 + 7x) * (6 + x)
(-7(6 + x) + 7x * (6 + x)) = 0
((6 * -7 + x * -7) + 7x * (6 + x)) = 0
((-42 + -7x) + 7x * (6 + x)) = 0
(-42 + -7x + (6 * 7x + x * 7x)) = 0
(-42 + -7x + (42x + 7x2)) = 0

Combine like terms: -7x + 42x = 35x
(-42 + 35x + 7x2) = 0

Solving
-42 + 35x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + 5x + x2) = 0

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

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-6, 1}