8x(2x-1)=24

Solution for 8x(2x-1)=24 equation:

Simplifying
8x(2x + -1) = 24

Reorder the terms:
8x(-1 + 2x) = 24
(-1 * 8x + 2x * 8x) = 24
(-8x + 16x2) = 24

Solving
-8x + 16x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -8x + 16x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -8x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + -1x + 2x2) = 0

Factor a trinomial.
8((-1 + -1x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}