0=-x^2+15x-36

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Solution for 0=-x^2+15x-36 equation: 


Simplifying
0 = -1x2 + 15x + -36

Reorder the terms:
0 = -36 + 15x + -1x2

Solving
0 = -36 + 15x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + -15x + x2 = -36 + 15x + -1x2 + 36 + -15x + x2

Reorder the terms:
36 + -15x + x2 = -36 + 36 + 15x + -15x + -1x2 + x2

Combine like terms: -36 + 36 = 0
36 + -15x + x2 = 0 + 15x + -15x + -1x2 + x2
36 + -15x + x2 = 15x + -15x + -1x2 + x2

Combine like terms: 15x + -15x = 0
36 + -15x + x2 = 0 + -1x2 + x2
36 + -15x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
36 + -15x + x2 = 0

Factor a trinomial.
(3 + -1x)(12 + -1x) = 0


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {3, 12}

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