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

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


Simplifying
2x + 5 = 2x2 + -1x + -15

Reorder the terms:
5 + 2x = 2x2 + -1x + -15

Reorder the terms:
5 + 2x = -15 + -1x + 2x2

Solving
5 + 2x = -15 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
5 + 15 + 2x + x + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: 5 + 15 = 20
20 + 2x + x + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: 2x + x = 3x
20 + 3x + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Reorder the terms:
20 + 3x + -2x2 = -15 + 15 + -1x + x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
20 + 3x + -2x2 = 0 + -1x + x + 2x2 + -2x2
20 + 3x + -2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
20 + 3x + -2x2 = 0 + 2x2 + -2x2
20 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 3x + -2x2 = 0

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


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
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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