(x+1)(x+5)+(x+5)(x-5)=(x+4)(x-5)

Solution for (x+1)(x+5)+(x+5)(x-5)=(x+4)(x-5) equation:

Simplifying
(x + 1)(x + 5) + (x + 5)(x + -5) = (x + 4)(x + -5)

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

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

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

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

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

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

Multiply (5 + x) * (-5 + x)
5 + 6x + x2 + (5(-5 + x) + x(-5 + x)) = (x + 4)(x + -5)
5 + 6x + x2 + ((-5 * 5 + x * 5) + x(-5 + x)) = (x + 4)(x + -5)
5 + 6x + x2 + ((-25 + 5x) + x(-5 + x)) = (x + 4)(x + -5)
5 + 6x + x2 + (-25 + 5x + (-5 * x + x * x)) = (x + 4)(x + -5)
5 + 6x + x2 + (-25 + 5x + (-5x + x2)) = (x + 4)(x + -5)

Combine like terms: 5x + -5x = 0
5 + 6x + x2 + (-25 + 0 + x2) = (x + 4)(x + -5)
5 + 6x + x2 + (-25 + x2) = (x + 4)(x + -5)

Reorder the terms:
5 + -25 + 6x + x2 + x2 = (x + 4)(x + -5)

Combine like terms: 5 + -25 = -20
-20 + 6x + x2 + x2 = (x + 4)(x + -5)

Combine like terms: x2 + x2 = 2x2
-20 + 6x + 2x2 = (x + 4)(x + -5)

Reorder the terms:
-20 + 6x + 2x2 = (4 + x)(x + -5)

Reorder the terms:
-20 + 6x + 2x2 = (4 + x)(-5 + x)

Multiply (4 + x) * (-5 + x)
-20 + 6x + 2x2 = (4(-5 + x) + x(-5 + x))
-20 + 6x + 2x2 = ((-5 * 4 + x * 4) + x(-5 + x))
-20 + 6x + 2x2 = ((-20 + 4x) + x(-5 + x))
-20 + 6x + 2x2 = (-20 + 4x + (-5 * x + x * x))
-20 + 6x + 2x2 = (-20 + 4x + (-5x + x2))

Combine like terms: 4x + -5x = -1x
-20 + 6x + 2x2 = (-20 + -1x + x2)

Add '20' to each side of the equation.
-20 + 6x + 20 + 2x2 = -20 + -1x + 20 + x2

Reorder the terms:
-20 + 20 + 6x + 2x2 = -20 + -1x + 20 + x2

Combine like terms: -20 + 20 = 0
0 + 6x + 2x2 = -20 + -1x + 20 + x2
6x + 2x2 = -20 + -1x + 20 + x2

Reorder the terms:
6x + 2x2 = -20 + 20 + -1x + x2

Combine like terms: -20 + 20 = 0
6x + 2x2 = 0 + -1x + x2
6x + 2x2 = -1x + x2

Solving
6x + 2x2 = -1x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0, -7}