-.5*32x^2+60x+6=56

Solution for -.5*32x^2+60x+6=56 equation:

Simplifying
-0.5 * 32x2 + 60x + 6 = 56

Multiply -0.5 * 32
-16x2 + 60x + 6 = 56

Reorder the terms:
6 + 60x + -16x2 = 56

Solving
6 + 60x + -16x2 = 56

Solving for variable 'x'.

Reorder the terms:
6 + -56 + 60x + -16x2 = 56 + -56

Combine like terms: 6 + -56 = -50
-50 + 60x + -16x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-50 + 60x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 30x + -8x2) = 0

Factor a trinomial.
2((-5 + 2x)(5 + -4x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 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 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {2.5, 1.25}