(x-2)(x+6)=-7

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

Simplifying
(x + -2)(x + 6) = -7

Reorder the terms:
(-2 + x)(x + 6) = -7

Reorder the terms:
(-2 + x)(6 + x) = -7

Multiply (-2 + x) * (6 + x)
(-2(6 + x) + x(6 + x)) = -7
((6 * -2 + x * -2) + x(6 + x)) = -7
((-12 + -2x) + x(6 + x)) = -7
(-12 + -2x + (6 * x + x * x)) = -7
(-12 + -2x + (6x + x2)) = -7

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) = -7

Solving
-12 + 4x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
-12 + 7 + 4x + x2 = -7 + 7

Combine like terms: -12 + 7 = -5
-5 + 4x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
-5 + 4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 1}