4x^2-24x=-32

Solution for 4x^2-24x=-32 equation:

Simplifying
4x2 + -24x = -32

Reorder the terms:
-24x + 4x2 = -32

Solving
-24x + 4x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + -24x + 4x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -6x + x2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}