-0.5*32x^2+24x+60=68

Solution for -0.5*32x^2+24x+60=68 equation:

Simplifying
-0.5 * 32x2 + 24x + 60 = 68

Multiply -0.5 * 32
-16x2 + 24x + 60 = 68

Reorder the terms:
60 + 24x + -16x2 = 68

Solving
60 + 24x + -16x2 = 68

Solving for variable 'x'.

Reorder the terms:
60 + -68 + 24x + -16x2 = 68 + -68

Combine like terms: 60 + -68 = -8
-8 + 24x + -16x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-8 + 24x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 3x + -2x2) = 0

Factor a trinomial.
8((-1 + x)(1 + -2x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {1, 0.5}