-2x^2-13x=-2x+15

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Solution for -2x^2-13x=-2x+15 equation: 


Simplifying
-2x2 + -13x = -2x + 15

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

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

Solving
-13x + -2x2 = 15 + -2x

Solving for variable 'x'.

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

Combine like terms: -13x + 2x = -11x
-15 + -11x + -2x2 = 15 + -2x + -15 + 2x

Reorder the terms:
-15 + -11x + -2x2 = 15 + -15 + -2x + 2x

Combine like terms: 15 + -15 = 0
-15 + -11x + -2x2 = 0 + -2x + 2x
-15 + -11x + -2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-15 + -11x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 11x + 2x2) = 0

Factor a trinomial.
-1((3 + x)(5 + 2x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-3, -2.5}

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