(x+1)(x-3)=(x+1)(2x+5)

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Solution for (x+1)(x-3)=(x+1)(2x+5) equation: 


Simplifying
(x + 1)(x + -3) = (x + 1)(2x + 5)

Reorder the terms:
(1 + x)(x + -3) = (x + 1)(2x + 5)

Reorder the terms:
(1 + x)(-3 + x) = (x + 1)(2x + 5)

Multiply (1 + x) * (-3 + x)
(1(-3 + x) + x(-3 + x)) = (x + 1)(2x + 5)
((-3 * 1 + x * 1) + x(-3 + x)) = (x + 1)(2x + 5)
((-3 + 1x) + x(-3 + x)) = (x + 1)(2x + 5)
(-3 + 1x + (-3 * x + x * x)) = (x + 1)(2x + 5)
(-3 + 1x + (-3x + x2)) = (x + 1)(2x + 5)

Combine like terms: 1x + -3x = -2x
(-3 + -2x + x2) = (x + 1)(2x + 5)

Reorder the terms:
-3 + -2x + x2 = (1 + x)(2x + 5)

Reorder the terms:
-3 + -2x + x2 = (1 + x)(5 + 2x)

Multiply (1 + x) * (5 + 2x)
-3 + -2x + x2 = (1(5 + 2x) + x(5 + 2x))
-3 + -2x + x2 = ((5 * 1 + 2x * 1) + x(5 + 2x))
-3 + -2x + x2 = ((5 + 2x) + x(5 + 2x))
-3 + -2x + x2 = (5 + 2x + (5 * x + 2x * x))
-3 + -2x + x2 = (5 + 2x + (5x + 2x2))

Combine like terms: 2x + 5x = 7x
-3 + -2x + x2 = (5 + 7x + 2x2)

Solving
-3 + -2x + x2 = 5 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + -2x + -7x + x2 + -2x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Combine like terms: -3 + -5 = -8
-8 + -2x + -7x + x2 + -2x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Combine like terms: -2x + -7x = -9x
-8 + -9x + x2 + -2x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-8 + -9x + -1x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Reorder the terms:
-8 + -9x + -1x2 = 5 + -5 + 7x + -7x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-8 + -9x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2
-8 + -9x + -1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-8 + -9x + -1x2 = 0 + 2x2 + -2x2
-8 + -9x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 9x + x2) = 0

Factor a trinomial.
-1((8 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

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 = {-8, -1}

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