-2x^2+32x=78

Solution for -2x^2+32x=78 equation:

Simplifying
-2x2 + 32x = 78

Reorder the terms:
32x + -2x2 = 78

Solving
32x + -2x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + 32x + -2x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 32x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + 16x + -1x2) = 0

Factor a trinomial.
2((-13 + x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + x)' equal to zero and attempt to solve:

Simplifying
-13 + x = 0

Solving
-13 + x = 0

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

Add '13' to each side of the equation.
-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x = 0 + 13
x = 0 + 13

Combine like terms: 0 + 13 = 13
x = 13

Simplifying
x = 13
Subproblem 2
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
Solution
x = {13, 3}