(x+2)(x+4)=13x+8

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Solution for (x+2)(x+4)=13x+8 equation: 


Simplifying
(x + 2)(x + 4) = 13x + 8

Reorder the terms:
(2 + x)(x + 4) = 13x + 8

Reorder the terms:
(2 + x)(4 + x) = 13x + 8

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) = 13x + 8
((4 * 2 + x * 2) + x(4 + x)) = 13x + 8
((8 + 2x) + x(4 + x)) = 13x + 8
(8 + 2x + (4 * x + x * x)) = 13x + 8
(8 + 2x + (4x + x2)) = 13x + 8

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) = 13x + 8

Reorder the terms:
8 + 6x + x2 = 8 + 13x

Add '-8' to each side of the equation.
8 + 6x + -8 + x2 = 8 + -8 + 13x

Reorder the terms:
8 + -8 + 6x + x2 = 8 + -8 + 13x

Combine like terms: 8 + -8 = 0
0 + 6x + x2 = 8 + -8 + 13x
6x + x2 = 8 + -8 + 13x

Combine like terms: 8 + -8 = 0
6x + x2 = 0 + 13x
6x + x2 = 13x

Solving
6x + x2 = 13x

Solving for variable 'x'.

Reorder the terms:
6x + -13x + x2 = 13x + -13x

Combine like terms: 6x + -13x = -7x
-7x + x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-7x + x2 = 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}

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