0=48+32x-16x^2

Solution for 0=48+32x-16x^2 equation:

Simplifying
0 = 48 + 32x + -16x2

Solving
0 = 48 + 32x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -48 = -48
-48 + -32x + 16x2 = 48 + 32x + -16x2 + -48 + -32x + 16x2

Reorder the terms:
-48 + -32x + 16x2 = 48 + -48 + 32x + -32x + -16x2 + 16x2

Combine like terms: 48 + -48 = 0
-48 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2
-48 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2

Combine like terms: 32x + -32x = 0
-48 + -32x + 16x2 = 0 + -16x2 + 16x2
-48 + -32x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-48 + -32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-3 + -2x + x2) = 0

Factor a trinomial.
16((-1 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}