5x+12=5x(x+2)+2

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Solution for 5x+12=5x(x+2)+2 equation: 


Simplifying
5x + 12 = 5x(x + 2) + 2

Reorder the terms:
12 + 5x = 5x(x + 2) + 2

Reorder the terms:
12 + 5x = 5x(2 + x) + 2
12 + 5x = (2 * 5x + x * 5x) + 2
12 + 5x = (10x + 5x2) + 2

Reorder the terms:
12 + 5x = 2 + 10x + 5x2

Solving
12 + 5x = 2 + 10x + 5x2

Solving for variable 'x'.

Reorder the terms:
12 + -2 + 5x + -10x + -5x2 = 2 + 10x + 5x2 + -2 + -10x + -5x2

Combine like terms: 12 + -2 = 10
10 + 5x + -10x + -5x2 = 2 + 10x + 5x2 + -2 + -10x + -5x2

Combine like terms: 5x + -10x = -5x
10 + -5x + -5x2 = 2 + 10x + 5x2 + -2 + -10x + -5x2

Reorder the terms:
10 + -5x + -5x2 = 2 + -2 + 10x + -10x + 5x2 + -5x2

Combine like terms: 2 + -2 = 0
10 + -5x + -5x2 = 0 + 10x + -10x + 5x2 + -5x2
10 + -5x + -5x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
10 + -5x + -5x2 = 0 + 5x2 + -5x2
10 + -5x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
10 + -5x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -1x + -1x2) = 0

Factor a trinomial.
5((1 + -1x)(2 + x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {1, -2}

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