=(x+7)(x+5)

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


Simplifying
0 = (x + 7)(x + 5)

Reorder the terms:
0 = (7 + x)(x + 5)

Reorder the terms:
0 = (7 + x)(5 + x)

Multiply (7 + x) * (5 + x)
0 = (7(5 + x) + x(5 + x))
0 = ((5 * 7 + x * 7) + x(5 + x))
0 = ((35 + 7x) + x(5 + x))
0 = (35 + 7x + (5 * x + x * x))
0 = (35 + 7x + (5x + x2))

Combine like terms: 7x + 5x = 12x
0 = (35 + 12x + x2)

Solving
0 = 35 + 12x + x2

Solving for variable 'x'.

Combine like terms: 0 + -35 = -35
-35 + -12x + -1x2 = 35 + 12x + x2 + -35 + -12x + -1x2

Reorder the terms:
-35 + -12x + -1x2 = 35 + -35 + 12x + -12x + x2 + -1x2

Combine like terms: 35 + -35 = 0
-35 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
-35 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-35 + -12x + -1x2 = 0 + x2 + -1x2
-35 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 12x + x2) = 0

Factor a trinomial.
-1((7 + x)(5 + x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-7, -5}

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