x(90-5x)=250+15x

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Solution for x(90-5x)=250+15x equation: 


Simplifying
x(90 + -5x) = 250 + 15x
(90 * x + -5x * x) = 250 + 15x
(90x + -5x2) = 250 + 15x

Solving
90x + -5x2 = 250 + 15x

Solving for variable 'x'.

Reorder the terms:
-250 + 90x + -15x + -5x2 = 250 + 15x + -250 + -15x

Combine like terms: 90x + -15x = 75x
-250 + 75x + -5x2 = 250 + 15x + -250 + -15x

Reorder the terms:
-250 + 75x + -5x2 = 250 + -250 + 15x + -15x

Combine like terms: 250 + -250 = 0
-250 + 75x + -5x2 = 0 + 15x + -15x
-250 + 75x + -5x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-250 + 75x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-50 + 15x + -1x2) = 0

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

Ignore the factor 5.

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 '(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 = {10, 5}

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