(x+5)(x-1)+(x+6)(x-1)=(x+7)(x-1)

Solution for (x+5)(x-1)+(x+6)(x-1)=(x+7)(x-1) equation:

Simplifying
(x + 5)(x + -1) + (x + 6)(x + -1) = (x + 7)(x + -1)

Reorder the terms:
(5 + x)(x + -1) + (x + 6)(x + -1) = (x + 7)(x + -1)

Reorder the terms:
(5 + x)(-1 + x) + (x + 6)(x + -1) = (x + 7)(x + -1)

Multiply (5 + x) * (-1 + x)
(5(-1 + x) + x(-1 + x)) + (x + 6)(x + -1) = (x + 7)(x + -1)
((-1 * 5 + x * 5) + x(-1 + x)) + (x + 6)(x + -1) = (x + 7)(x + -1)
((-5 + 5x) + x(-1 + x)) + (x + 6)(x + -1) = (x + 7)(x + -1)
(-5 + 5x + (-1 * x + x * x)) + (x + 6)(x + -1) = (x + 7)(x + -1)
(-5 + 5x + (-1x + x2)) + (x + 6)(x + -1) = (x + 7)(x + -1)

Combine like terms: 5x + -1x = 4x
(-5 + 4x + x2) + (x + 6)(x + -1) = (x + 7)(x + -1)

Reorder the terms:
-5 + 4x + x2 + (6 + x)(x + -1) = (x + 7)(x + -1)

Reorder the terms:
-5 + 4x + x2 + (6 + x)(-1 + x) = (x + 7)(x + -1)

Multiply (6 + x) * (-1 + x)
-5 + 4x + x2 + (6(-1 + x) + x(-1 + x)) = (x + 7)(x + -1)
-5 + 4x + x2 + ((-1 * 6 + x * 6) + x(-1 + x)) = (x + 7)(x + -1)
-5 + 4x + x2 + ((-6 + 6x) + x(-1 + x)) = (x + 7)(x + -1)
-5 + 4x + x2 + (-6 + 6x + (-1 * x + x * x)) = (x + 7)(x + -1)
-5 + 4x + x2 + (-6 + 6x + (-1x + x2)) = (x + 7)(x + -1)

Combine like terms: 6x + -1x = 5x
-5 + 4x + x2 + (-6 + 5x + x2) = (x + 7)(x + -1)

Reorder the terms:
-5 + -6 + 4x + 5x + x2 + x2 = (x + 7)(x + -1)

Combine like terms: -5 + -6 = -11
-11 + 4x + 5x + x2 + x2 = (x + 7)(x + -1)

Combine like terms: 4x + 5x = 9x
-11 + 9x + x2 + x2 = (x + 7)(x + -1)

Combine like terms: x2 + x2 = 2x2
-11 + 9x + 2x2 = (x + 7)(x + -1)

Reorder the terms:
-11 + 9x + 2x2 = (7 + x)(x + -1)

Reorder the terms:
-11 + 9x + 2x2 = (7 + x)(-1 + x)

Multiply (7 + x) * (-1 + x)
-11 + 9x + 2x2 = (7(-1 + x) + x(-1 + x))
-11 + 9x + 2x2 = ((-1 * 7 + x * 7) + x(-1 + x))
-11 + 9x + 2x2 = ((-7 + 7x) + x(-1 + x))
-11 + 9x + 2x2 = (-7 + 7x + (-1 * x + x * x))
-11 + 9x + 2x2 = (-7 + 7x + (-1x + x2))

Combine like terms: 7x + -1x = 6x
-11 + 9x + 2x2 = (-7 + 6x + x2)

Solving
-11 + 9x + 2x2 = -7 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-11 + 7 + 9x + -6x + 2x2 + -1x2 = -7 + 6x + x2 + 7 + -6x + -1x2

Combine like terms: -11 + 7 = -4
-4 + 9x + -6x + 2x2 + -1x2 = -7 + 6x + x2 + 7 + -6x + -1x2

Combine like terms: 9x + -6x = 3x
-4 + 3x + 2x2 + -1x2 = -7 + 6x + x2 + 7 + -6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + 3x + 1x2 = -7 + 6x + x2 + 7 + -6x + -1x2

Reorder the terms:
-4 + 3x + 1x2 = -7 + 7 + 6x + -6x + x2 + -1x2

Combine like terms: -7 + 7 = 0
-4 + 3x + 1x2 = 0 + 6x + -6x + x2 + -1x2
-4 + 3x + 1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-4 + 3x + 1x2 = 0 + x2 + -1x2
-4 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 1}