15(x+36)+15x=2x(x+36)

Solution for 15(x+36)+15x=2x(x+36) equation:

Simplifying
15(x + 36) + 15x = 2x(x + 36)

Reorder the terms:
15(36 + x) + 15x = 2x(x + 36)
(36 * 15 + x * 15) + 15x = 2x(x + 36)
(540 + 15x) + 15x = 2x(x + 36)

Combine like terms: 15x + 15x = 30x
540 + 30x = 2x(x + 36)

Reorder the terms:
540 + 30x = 2x(36 + x)
540 + 30x = (36 * 2x + x * 2x)
540 + 30x = (72x + 2x2)

Solving
540 + 30x = 72x + 2x2

Solving for variable 'x'.

Combine like terms: 30x + -72x = -42x
540 + -42x + -2x2 = 72x + 2x2 + -72x + -2x2

Reorder the terms:
540 + -42x + -2x2 = 72x + -72x + 2x2 + -2x2

Combine like terms: 72x + -72x = 0
540 + -42x + -2x2 = 0 + 2x2 + -2x2
540 + -42x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
540 + -42x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(270 + -21x + -1x2) = 0

Factor a trinomial.
2((9 + -1x)(30 + x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 0

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

Add '-30' to each side of the equation.
30 + -30 + x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + x = 0 + -30
x = 0 + -30

Combine like terms: 0 + -30 = -30
x = -30

Simplifying
x = -30
Solution
x = {9, -30}