7x^2-3x+15=5x+6x^2

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Solution for 7x^2-3x+15=5x+6x^2 equation: 


Simplifying
7x2 + -3x + 15 = 5x + 6x2

Reorder the terms:
15 + -3x + 7x2 = 5x + 6x2

Solving
15 + -3x + 7x2 = 5x + 6x2

Solving for variable 'x'.

Reorder the terms:
15 + -3x + -5x + 7x2 + -6x2 = 5x + 6x2 + -5x + -6x2

Combine like terms: -3x + -5x = -8x
15 + -8x + 7x2 + -6x2 = 5x + 6x2 + -5x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
15 + -8x + 1x2 = 5x + 6x2 + -5x + -6x2

Reorder the terms:
15 + -8x + 1x2 = 5x + -5x + 6x2 + -6x2

Combine like terms: 5x + -5x = 0
15 + -8x + 1x2 = 0 + 6x2 + -6x2
15 + -8x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
15 + -8x + 1x2 = 0

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


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, 5}

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