-.5(32)*x^2+(20)*x+3=9

Solution for -.5(32)*x^2+(20)*x+3=9 equation:

Simplifying
-0.5(32) * x2 + (20) * x + 3 = 9

Multiply -0.5 * 32
-16x2 + (20) * x + 3 = 9

Reorder the terms:
3 + 20x + -16x2 = 9

Solving
3 + 20x + -16x2 = 9

Solving for variable 'x'.

Reorder the terms:
3 + -9 + 20x + -16x2 = 9 + -9

Combine like terms: 3 + -9 = -6
-6 + 20x + -16x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-6 + 20x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 10x + -8x2) = 0

Factor a trinomial.
2((-3 + 4x)(1 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 4x)' equal to zero and attempt to solve:

Simplifying
-3 + 4x = 0

Solving
-3 + 4x = 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 + 4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4x = 0 + 3
4x = 0 + 3

Combine like terms: 0 + 3 = 3
4x = 3

Divide each side by '4'.
x = 0.75

Simplifying
x = 0.75
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 = {0.75, 0.5}