4x(6x-2)=32

Solution for 4x(6x-2)=32 equation:

Simplifying
4x(6x + -2) = 32

Reorder the terms:
4x(-2 + 6x) = 32
(-2 * 4x + 6x * 4x) = 32
(-8x + 24x2) = 32

Solving
-8x + 24x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + -8x + 24x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -8x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + -1x + 3x2) = 0

Factor a trinomial.
8((-1 + -1x)(4 + -3x)) = 0

Ignore the factor 8.
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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-1, 1.333333333}