68=-.5*32x^2+24x+60

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Solution for 68=-.5*32x^2+24x+60 equation: 


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

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

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

Solving
68 = 60 + 24x + -16x2

Solving for variable 'x'.

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

Reorder the terms:
8 + -24x + 16x2 = 60 + -60 + 24x + -24x + -16x2 + 16x2

Combine like terms: 60 + -60 = 0
8 + -24x + 16x2 = 0 + 24x + -24x + -16x2 + 16x2
8 + -24x + 16x2 = 24x + -24x + -16x2 + 16x2

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

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

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

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

Ignore the factor 8.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

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

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