32=-16(x-2)(x+1)

Solution for 32=-16(x-2)(x+1) equation:

Simplifying
32 = -16(x + -2)(x + 1)

Reorder the terms:
32 = -16(-2 + x)(x + 1)

Reorder the terms:
32 = -16(-2 + x)(1 + x)

Multiply (-2 + x) * (1 + x)
32 = -16(-2(1 + x) + x(1 + x))
32 = -16((1 * -2 + x * -2) + x(1 + x))
32 = -16((-2 + -2x) + x(1 + x))
32 = -16(-2 + -2x + (1 * x + x * x))
32 = -16(-2 + -2x + (1x + x2))

Combine like terms: -2x + 1x = -1x
32 = -16(-2 + -1x + x2)
32 = (-2 * -16 + -1x * -16 + x2 * -16)
32 = (32 + 16x + -16x2)

Add '-32' to each side of the equation.
32 + -32 = 32 + 16x + -32 + -16x2

Combine like terms: 32 + -32 = 0
0 = 32 + 16x + -32 + -16x2

Reorder the terms:
0 = 32 + -32 + 16x + -16x2

Combine like terms: 32 + -32 = 0
0 = 0 + 16x + -16x2
0 = 16x + -16x2

Solving
0 = 16x + -16x2

Solving for variable 'x'.
Remove the zero:
-16x + 16x2 = 16x + -16x2 + -16x + 16x2

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

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

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

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

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}