5x^2+13x+12=x+5

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Solution for 5x^2+13x+12=x+5 equation: 


Simplifying
5x2 + 13x + 12 = x + 5

Reorder the terms:
12 + 13x + 5x2 = x + 5

Reorder the terms:
12 + 13x + 5x2 = 5 + x

Solving
12 + 13x + 5x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
12 + -5 + 13x + -1x + 5x2 = 5 + x + -5 + -1x

Combine like terms: 12 + -5 = 7
7 + 13x + -1x + 5x2 = 5 + x + -5 + -1x

Combine like terms: 13x + -1x = 12x
7 + 12x + 5x2 = 5 + x + -5 + -1x

Reorder the terms:
7 + 12x + 5x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
7 + 12x + 5x2 = 0 + x + -1x
7 + 12x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
7 + 12x + 5x2 = 0

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


Subproblem 1
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4

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 = {-1.4, -1}

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