=(x+7)(x+1)

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Solution for =(x+7)(x+1) equation: 


Simplifying
0 = (x + 7)(x + 1)

Reorder the terms:
0 = (7 + x)(x + 1)

Reorder the terms:
0 = (7 + x)(1 + x)

Multiply (7 + x) * (1 + x)
0 = (7(1 + x) + x(1 + x))
0 = ((1 * 7 + x * 7) + x(1 + x))
0 = ((7 + 7x) + x(1 + x))
0 = (7 + 7x + (1 * x + x * x))
0 = (7 + 7x + (1x + x2))

Combine like terms: 7x + 1x = 8x
0 = (7 + 8x + x2)

Solving
0 = 7 + 8x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 8x + x2) = 0

Factor a trinomial.
-1((7 + x)(1 + 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 '(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 = {-7, -1}

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