32=48X-16X^2

Solution for 32=48X-16X^2 equation:

Simplifying
32 = 48X + -16X2

Solving
32 = 48X + -16X2

Solving for variable 'X'.

Reorder the terms:
32 + -48X + 16X2 = 48X + -48X + -16X2 + 16X2

Combine like terms: 48X + -48X = 0
32 + -48X + 16X2 = 0 + -16X2 + 16X2
32 + -48X + 16X2 = -16X2 + 16X2

Combine like terms: -16X2 + 16X2 = 0
32 + -48X + 16X2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(2 + -3X + X2) = 0

Factor a trinomial.
16((1 + -1X)(2 + -1X)) = 0

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

Simplifying
1 + -1X = 0

Solving
1 + -1X = 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 + -1X = 0 + -1

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

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

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Subproblem 2
Set the factor '(2 + -1X)' equal to zero and attempt to solve:

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Solution
X = {1, 2}