2x^2+54=x^2+15x

Solution for 2x^2+54=x^2+15x equation:

Simplifying
2x2 + 54 = x2 + 15x

Reorder the terms:
54 + 2x2 = x2 + 15x

Reorder the terms:
54 + 2x2 = 15x + x2

Solving
54 + 2x2 = 15x + x2

Solving for variable 'x'.

Reorder the terms:
54 + -15x + 2x2 + -1x2 = 15x + x2 + -15x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
54 + -15x + 1x2 = 15x + x2 + -15x + -1x2

Reorder the terms:
54 + -15x + 1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
54 + -15x + 1x2 = 0 + x2 + -1x2
54 + -15x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
54 + -15x + 1x2 = 0

Factor a trinomial.
(6 + -1x)(9 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {6, 9}