2x^2+13x+15=3x+7

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Solution for 2x^2+13x+15=3x+7 equation: 


Simplifying
2x2 + 13x + 15 = 3x + 7

Reorder the terms:
15 + 13x + 2x2 = 3x + 7

Reorder the terms:
15 + 13x + 2x2 = 7 + 3x

Solving
15 + 13x + 2x2 = 7 + 3x

Solving for variable 'x'.

Reorder the terms:
15 + -7 + 13x + -3x + 2x2 = 7 + 3x + -7 + -3x

Combine like terms: 15 + -7 = 8
8 + 13x + -3x + 2x2 = 7 + 3x + -7 + -3x

Combine like terms: 13x + -3x = 10x
8 + 10x + 2x2 = 7 + 3x + -7 + -3x

Reorder the terms:
8 + 10x + 2x2 = 7 + -7 + 3x + -3x

Combine like terms: 7 + -7 = 0
8 + 10x + 2x2 = 0 + 3x + -3x
8 + 10x + 2x2 = 3x + -3x

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

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5x + x2) = 0

Factor a trinomial.
2((4 + x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -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 = {-4, -1}

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