5x^2+2x+15=4x^2+13x-15

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Solution for 5x^2+2x+15=4x^2+13x-15 equation: 


Simplifying
5x2 + 2x + 15 = 4x2 + 13x + -15

Reorder the terms:
15 + 2x + 5x2 = 4x2 + 13x + -15

Reorder the terms:
15 + 2x + 5x2 = -15 + 13x + 4x2

Solving
15 + 2x + 5x2 = -15 + 13x + 4x2

Solving for variable 'x'.

Reorder the terms:
15 + 15 + 2x + -13x + 5x2 + -4x2 = -15 + 13x + 4x2 + 15 + -13x + -4x2

Combine like terms: 15 + 15 = 30
30 + 2x + -13x + 5x2 + -4x2 = -15 + 13x + 4x2 + 15 + -13x + -4x2

Combine like terms: 2x + -13x = -11x
30 + -11x + 5x2 + -4x2 = -15 + 13x + 4x2 + 15 + -13x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
30 + -11x + 1x2 = -15 + 13x + 4x2 + 15 + -13x + -4x2

Reorder the terms:
30 + -11x + 1x2 = -15 + 15 + 13x + -13x + 4x2 + -4x2

Combine like terms: -15 + 15 = 0
30 + -11x + 1x2 = 0 + 13x + -13x + 4x2 + -4x2
30 + -11x + 1x2 = 13x + -13x + 4x2 + -4x2

Combine like terms: 13x + -13x = 0
30 + -11x + 1x2 = 0 + 4x2 + -4x2
30 + -11x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
30 + -11x + 1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {5, 6}

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