4x^2-24x+32=1292

Solution for 4x^2-24x+32=1292 equation:

Simplifying
4x2 + -24x + 32 = 1292

Reorder the terms:
32 + -24x + 4x2 = 1292

Solving
32 + -24x + 4x2 = 1292

Solving for variable 'x'.

Reorder the terms:
32 + -1292 + -24x + 4x2 = 1292 + -1292

Combine like terms: 32 + -1292 = -1260
-1260 + -24x + 4x2 = 1292 + -1292

Combine like terms: 1292 + -1292 = 0
-1260 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-315 + -6x + x2) = 0

Factor a trinomial.
4((-15 + -1x)(21 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-15, 21}