=(5-1x)(50+30x)

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Solution for =(5-1x)(50+30x) equation: 


Simplifying
0 = (5 + -1x)(50 + 30x)

Multiply (5 + -1x) * (50 + 30x)
0 = (5(50 + 30x) + -1x * (50 + 30x))
0 = ((50 * 5 + 30x * 5) + -1x * (50 + 30x))
0 = ((250 + 150x) + -1x * (50 + 30x))
0 = (250 + 150x + (50 * -1x + 30x * -1x))
0 = (250 + 150x + (-50x + -30x2))

Combine like terms: 150x + -50x = 100x
0 = (250 + 100x + -30x2)

Solving
0 = 250 + 100x + -30x2

Solving for variable 'x'.

Combine like terms: 0 + -250 = -250
-250 + -100x + 30x2 = 250 + 100x + -30x2 + -250 + -100x + 30x2

Reorder the terms:
-250 + -100x + 30x2 = 250 + -250 + 100x + -100x + -30x2 + 30x2

Combine like terms: 250 + -250 = 0
-250 + -100x + 30x2 = 0 + 100x + -100x + -30x2 + 30x2
-250 + -100x + 30x2 = 100x + -100x + -30x2 + 30x2

Combine like terms: 100x + -100x = 0
-250 + -100x + 30x2 = 0 + -30x2 + 30x2
-250 + -100x + 30x2 = -30x2 + 30x2

Combine like terms: -30x2 + 30x2 = 0
-250 + -100x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-25 + -10x + 3x2) = 0

Factor a trinomial.
10((-5 + -3x)(5 + -1x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1.666666667, 5}

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