-4x^2+32x=48

Solution for -4x^2+32x=48 equation:

Simplifying
-4x2 + 32x = 48

Reorder the terms:
32x + -4x2 = 48

Solving
32x + -4x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 32x + -4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 32x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 8x + -1x2) = 0

Factor a trinomial.
4((-6 + x)(2 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 2}