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

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


Simplifying
0 = (10 + x)(15 + 2x)

Multiply (10 + x) * (15 + 2x)
0 = (10(15 + 2x) + x(15 + 2x))
0 = ((15 * 10 + 2x * 10) + x(15 + 2x))
0 = ((150 + 20x) + x(15 + 2x))
0 = (150 + 20x + (15 * x + 2x * x))
0 = (150 + 20x + (15x + 2x2))

Combine like terms: 20x + 15x = 35x
0 = (150 + 35x + 2x2)

Solving
0 = 150 + 35x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -150 = -150
-150 + -35x + -2x2 = 150 + 35x + 2x2 + -150 + -35x + -2x2

Reorder the terms:
-150 + -35x + -2x2 = 150 + -150 + 35x + -35x + 2x2 + -2x2

Combine like terms: 150 + -150 = 0
-150 + -35x + -2x2 = 0 + 35x + -35x + 2x2 + -2x2
-150 + -35x + -2x2 = 35x + -35x + 2x2 + -2x2

Combine like terms: 35x + -35x = 0
-150 + -35x + -2x2 = 0 + 2x2 + -2x2
-150 + -35x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-150 + -35x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(150 + 35x + 2x2) = 0

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

Ignore the factor -1.

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

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

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

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

Simplifying
x = -10

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

Simplifying
15 + 2x = 0

Solving
15 + 2x = 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 + 2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2x = 0 + -15
2x = 0 + -15

Combine like terms: 0 + -15 = -15
2x = -15

Divide each side by '2'.
x = -7.5

Simplifying
x = -7.5
Solution
x = {-10, -7.5}

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