-0.5*32x^2+2000x+0=-6144

Solution for -0.5*32x^2+2000x+0=-6144 equation:

Simplifying
-0.5 * 32x2 + 2000x + 0 = -6144

Multiply -0.5 * 32
-16x2 + 2000x + 0 = -6144

Reorder the terms:
0 + 2000x + -16x2 = -6144
Remove the zero:
2000x + -16x2 = -6144

Solving
2000x + -16x2 = -6144

Solving for variable 'x'.

Reorder the terms:
6144 + 2000x + -16x2 = -6144 + 6144

Combine like terms: -6144 + 6144 = 0
6144 + 2000x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(384 + 125x + -1x2) = 0

Factor a trinomial.
16((128 + -1x)(3 + x)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(128 + -1x)' equal to zero and attempt to solve:

Simplifying
128 + -1x = 0

Solving
128 + -1x = 0

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

Add '-128' to each side of the equation.
128 + -128 + -1x = 0 + -128

Combine like terms: 128 + -128 = 0
0 + -1x = 0 + -128
-1x = 0 + -128

Combine like terms: 0 + -128 = -128
-1x = -128

Divide each side by '-1'.
x = 128

Simplifying
x = 128
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {128, -3}