150=(30+2x)(10-.5x)

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Solution for 150=(30+2x)(10-.5x) equation: 


Simplifying
150 = (30 + 2x)(10 + -0.5x)

Multiply (30 + 2x) * (10 + -0.5x)
150 = (30(10 + -0.5x) + 2x * (10 + -0.5x))
150 = ((10 * 30 + -0.5x * 30) + 2x * (10 + -0.5x))
150 = ((300 + -15x) + 2x * (10 + -0.5x))
150 = (300 + -15x + (10 * 2x + -0.5x * 2x))
150 = (300 + -15x + (20x + -1x2))

Combine like terms: -15x + 20x = 5x
150 = (300 + 5x + -1x2)

Solving
150 = 300 + 5x + -1x2

Solving for variable 'x'.

Combine like terms: 150 + -300 = -150
-150 + -5x + x2 = 300 + 5x + -1x2 + -300 + -5x + x2

Reorder the terms:
-150 + -5x + x2 = 300 + -300 + 5x + -5x + -1x2 + x2

Combine like terms: 300 + -300 = 0
-150 + -5x + x2 = 0 + 5x + -5x + -1x2 + x2
-150 + -5x + x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-150 + -5x + x2 = 0 + -1x2 + x2
-150 + -5x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-150 + -5x + x2 = 0

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


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 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 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 + -1x = 0 + -15

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

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

Divide each side by '-1'.
x = 15

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

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