4x^2-32x=-28

Solution for 4x^2-32x=-28 equation:

Simplifying
4x2 + -32x = -28

Reorder the terms:
-32x + 4x2 = -28

Solving
-32x + 4x2 = -28

Solving for variable 'x'.

Reorder the terms:
28 + -32x + 4x2 = -28 + 28

Combine like terms: -28 + 28 = 0
28 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -8x + x2) = 0

Factor a trinomial.
4((1 + -1x)(7 + -1x)) = 0

Ignore the factor 4.
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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}