x-5=2x^2+14x+15

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Solution for x-5=2x^2+14x+15 equation: 


Simplifying
x + -5 = 2x2 + 14x + 15

Reorder the terms:
-5 + x = 2x2 + 14x + 15

Reorder the terms:
-5 + x = 15 + 14x + 2x2

Solving
-5 + x = 15 + 14x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + -15 + x + -14x + -2x2 = 15 + 14x + 2x2 + -15 + -14x + -2x2

Combine like terms: -5 + -15 = -20
-20 + x + -14x + -2x2 = 15 + 14x + 2x2 + -15 + -14x + -2x2

Combine like terms: x + -14x = -13x
-20 + -13x + -2x2 = 15 + 14x + 2x2 + -15 + -14x + -2x2

Reorder the terms:
-20 + -13x + -2x2 = 15 + -15 + 14x + -14x + 2x2 + -2x2

Combine like terms: 15 + -15 = 0
-20 + -13x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2
-20 + -13x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
-20 + -13x + -2x2 = 0 + 2x2 + -2x2
-20 + -13x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-20 + -13x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 13x + 2x2) = 0

Factor a trinomial.
-1((4 + x)(5 + 2x)) = 0

Ignore the factor -1.

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 '(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 = {-4, -2.5}

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