-.5(32x^2)+24x+6=6

Solution for -.5(32x^2)+24x+6=6 equation:

Simplifying
-0.5(32x2) + 24x + 6 = 6

Remove parenthesis around (32x2)
-0.5 * 32x2 + 24x + 6 = 6

Multiply -0.5 * 32
-16x2 + 24x + 6 = 6

Reorder the terms:
6 + 24x + -16x2 = 6

Add '-6' to each side of the equation.
6 + 24x + -6 + -16x2 = 6 + -6

Reorder the terms:
6 + -6 + 24x + -16x2 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + 24x + -16x2 = 6 + -6
24x + -16x2 = 6 + -6

Combine like terms: 6 + -6 = 0
24x + -16x2 = 0

Solving
24x + -16x2 = 0

Solving for variable 'x'.

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

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.5}