150=(2x+15)(2x+10)

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Solution for 150=(2x+15)(2x+10) equation: 


Simplifying
150 = (2x + 15)(2x + 10)

Reorder the terms:
150 = (15 + 2x)(2x + 10)

Reorder the terms:
150 = (15 + 2x)(10 + 2x)

Multiply (15 + 2x) * (10 + 2x)
150 = (15(10 + 2x) + 2x * (10 + 2x))
150 = ((10 * 15 + 2x * 15) + 2x * (10 + 2x))
150 = ((150 + 30x) + 2x * (10 + 2x))
150 = (150 + 30x + (10 * 2x + 2x * 2x))
150 = (150 + 30x + (20x + 4x2))

Combine like terms: 30x + 20x = 50x
150 = (150 + 50x + 4x2)

Add '-150' to each side of the equation.
150 + -150 = 150 + 50x + -150 + 4x2

Combine like terms: 150 + -150 = 0
0 = 150 + 50x + -150 + 4x2

Reorder the terms:
0 = 150 + -150 + 50x + 4x2

Combine like terms: 150 + -150 = 0
0 = 0 + 50x + 4x2
0 = 50x + 4x2

Solving
0 = 50x + 4x2

Solving for variable 'x'.
Remove the zero:
-50x + -4x2 = 50x + 4x2 + -50x + -4x2

Reorder the terms:
-50x + -4x2 = 50x + -50x + 4x2 + -4x2

Combine like terms: 50x + -50x = 0
-50x + -4x2 = 0 + 4x2 + -4x2
-50x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-50x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(25 + 2x) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(25 + 2x)' equal to zero and attempt to solve:

Simplifying
25 + 2x = 0

Solving
25 + 2x = 0

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

Add '-25' to each side of the equation.
25 + -25 + 2x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 2x = 0 + -25
2x = 0 + -25

Combine like terms: 0 + -25 = -25
2x = -25

Divide each side by '2'.
x = -12.5

Simplifying
x = -12.5
Solution
x = {0, -12.5}

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