0=15x+50-5x^2

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Solution for 0=15x+50-5x^2 equation: 


Simplifying
0 = 15x + 50 + -5x2

Reorder the terms:
0 = 50 + 15x + -5x2

Solving
0 = 50 + 15x + -5x2

Solving for variable 'x'.

Combine like terms: 0 + -50 = -50
-50 + -15x + 5x2 = 50 + 15x + -5x2 + -50 + -15x + 5x2

Reorder the terms:
-50 + -15x + 5x2 = 50 + -50 + 15x + -15x + -5x2 + 5x2

Combine like terms: 50 + -50 = 0
-50 + -15x + 5x2 = 0 + 15x + -15x + -5x2 + 5x2
-50 + -15x + 5x2 = 15x + -15x + -5x2 + 5x2

Combine like terms: 15x + -15x = 0
-50 + -15x + 5x2 = 0 + -5x2 + 5x2
-50 + -15x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-50 + -15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -3x + x2) = 0

Factor a trinomial.
5((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 5}

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