15(x+20)+15x=2x(x+20)

Solution for 15(x+20)+15x=2x(x+20) equation:

Simplifying
15(x + 20) + 15x = 2x(x + 20)

Reorder the terms:
15(20 + x) + 15x = 2x(x + 20)
(20 * 15 + x * 15) + 15x = 2x(x + 20)
(300 + 15x) + 15x = 2x(x + 20)

Combine like terms: 15x + 15x = 30x
300 + 30x = 2x(x + 20)

Reorder the terms:
300 + 30x = 2x(20 + x)
300 + 30x = (20 * 2x + x * 2x)
300 + 30x = (40x + 2x2)

Solving
300 + 30x = 40x + 2x2

Solving for variable 'x'.

Combine like terms: 30x + -40x = -10x
300 + -10x + -2x2 = 40x + 2x2 + -40x + -2x2

Reorder the terms:
300 + -10x + -2x2 = 40x + -40x + 2x2 + -2x2

Combine like terms: 40x + -40x = 0
300 + -10x + -2x2 = 0 + 2x2 + -2x2
300 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
300 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(150 + -5x + -1x2) = 0

Factor a trinomial.
2((10 + -1x)(15 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {10, -15}