0=(x+1)(x+3)

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Solution for 0=(x+1)(x+3) equation: 


Simplifying
0 = (x + 1)(x + 3)

Reorder the terms:
0 = (1 + x)(x + 3)

Reorder the terms:
0 = (1 + x)(3 + x)

Multiply (1 + x) * (3 + x)
0 = (1(3 + x) + x(3 + x))
0 = ((3 * 1 + x * 1) + x(3 + x))
0 = ((3 + 1x) + x(3 + x))
0 = (3 + 1x + (3 * x + x * x))
0 = (3 + 1x + (3x + x2))

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

Solving
0 = 3 + 4x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 4x + x2) = 0

Factor a trinomial.
-1((3 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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 = {-3, -1}

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