0=-x^2+14x-45

Solution for 0=-x^2+14x-45 equation:

Simplifying
0 = -1x2 + 14x + -45

Reorder the terms:
0 = -45 + 14x + -1x2

Solving
0 = -45 + 14x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 45 = 45
45 + -14x + x2 = -45 + 14x + -1x2 + 45 + -14x + x2

Reorder the terms:
45 + -14x + x2 = -45 + 45 + 14x + -14x + -1x2 + x2

Combine like terms: -45 + 45 = 0
45 + -14x + x2 = 0 + 14x + -14x + -1x2 + x2
45 + -14x + x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
45 + -14x + x2 = 0 + -1x2 + x2
45 + -14x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
45 + -14x + x2 = 0

Factor a trinomial.
(5 + -1x)(9 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {5, 9}