(x-1)(x+5)=7

Solution for (x-1)(x+5)=7 equation:

Simplifying
(x + -1)(x + 5) = 7

Reorder the terms:
(-1 + x)(x + 5) = 7

Reorder the terms:
(-1 + x)(5 + x) = 7

Multiply (-1 + x) * (5 + x)
(-1(5 + x) + x(5 + x)) = 7
((5 * -1 + x * -1) + x(5 + x)) = 7
((-5 + -1x) + x(5 + x)) = 7
(-5 + -1x + (5 * x + x * x)) = 7
(-5 + -1x + (5x + x2)) = 7

Combine like terms: -1x + 5x = 4x
(-5 + 4x + x2) = 7

Solving
-5 + 4x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-5 + -7 + 4x + x2 = 7 + -7

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

Combine like terms: 7 + -7 = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6, 2}