3x^2+12x+13=2x+5

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Solution for 3x^2+12x+13=2x+5 equation: 


Simplifying
3x2 + 12x + 13 = 2x + 5

Reorder the terms:
13 + 12x + 3x2 = 2x + 5

Reorder the terms:
13 + 12x + 3x2 = 5 + 2x

Solving
13 + 12x + 3x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
13 + -5 + 12x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: 13 + -5 = 8
8 + 12x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: 12x + -2x = 10x
8 + 10x + 3x2 = 5 + 2x + -5 + -2x

Reorder the terms:
8 + 10x + 3x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
8 + 10x + 3x2 = 0 + 2x + -2x
8 + 10x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
8 + 10x + 3x2 = 0

Factor a trinomial.
(2 + x)(4 + 3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-2, -1.333333333}

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