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

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


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

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

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

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

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

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

Solving
-5 + 4x + x2 = -7 + x

Solving for variable 'x'.

Reorder the terms:
-5 + 7 + 4x + -1x + x2 = -7 + x + 7 + -1x

Combine like terms: -5 + 7 = 2
2 + 4x + -1x + x2 = -7 + x + 7 + -1x

Combine like terms: 4x + -1x = 3x
2 + 3x + x2 = -7 + x + 7 + -1x

Reorder the terms:
2 + 3x + x2 = -7 + 7 + x + -1x

Combine like terms: -7 + 7 = 0
2 + 3x + x2 = 0 + x + -1x
2 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
2 + 3x + x2 = 0

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


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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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