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

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


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

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

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

Solving
56 = 6 + 60x + -16x2

Solving for variable 'x'.

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

Reorder the terms:
50 + -60x + 16x2 = 6 + -6 + 60x + -60x + -16x2 + 16x2

Combine like terms: 6 + -6 = 0
50 + -60x + 16x2 = 0 + 60x + -60x + -16x2 + 16x2
50 + -60x + 16x2 = 60x + -60x + -16x2 + 16x2

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

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

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

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {1.25, 2.5}

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