6x^2-38x=-32

Solution for 6x^2-38x=-32 equation:

Simplifying
6x2 + -38x = -32

Reorder the terms:
-38x + 6x2 = -32

Solving
-38x + 6x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + -38x + 6x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -38x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -19x + 3x2) = 0

Factor a trinomial.
2((1 + -1x)(16 + -3x)) = 0

Ignore the factor 2.
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 '(16 + -3x)' equal to zero and attempt to solve:

Simplifying
16 + -3x = 0

Solving
16 + -3x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3x = 0 + -16
-3x = 0 + -16

Combine like terms: 0 + -16 = -16
-3x = -16

Divide each side by '-3'.
x = 5.333333333

Simplifying
x = 5.333333333
Solution
x = {1, 5.333333333}