0=-2x^2+34x-60

Solution for 0=-2x^2+34x-60 equation:

Simplifying
0 = -2x2 + 34x + -60

Reorder the terms:
0 = -60 + 34x + -2x2

Solving
0 = -60 + 34x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 60 = 60
60 + -34x + 2x2 = -60 + 34x + -2x2 + 60 + -34x + 2x2

Reorder the terms:
60 + -34x + 2x2 = -60 + 60 + 34x + -34x + -2x2 + 2x2

Combine like terms: -60 + 60 = 0
60 + -34x + 2x2 = 0 + 34x + -34x + -2x2 + 2x2
60 + -34x + 2x2 = 34x + -34x + -2x2 + 2x2

Combine like terms: 34x + -34x = 0
60 + -34x + 2x2 = 0 + -2x2 + 2x2
60 + -34x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
60 + -34x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -17x + x2) = 0

Factor a trinomial.
2((2 + -1x)(15 + -1x)) = 0

Ignore the factor 2.
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 '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

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

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

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {2, 15}