-24X^2+24X-6=0

Solution for -24X^2+24X-6=0 equation:

Simplifying
-24X2 + 24X + -6 = 0

Reorder the terms:
-6 + 24X + -24X2 = 0

Solving
-6 + 24X + -24X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 4X + -4X2) = 0

Factor a trinomial.
6((-1 + 2X)(1 + -2X)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + 2X)' equal to zero and attempt to solve:

Simplifying
-1 + 2X = 0

Solving
-1 + 2X = 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 + 2X = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2X = 0 + 1
2X = 0 + 1

Combine like terms: 0 + 1 = 1
2X = 1

Divide each side by '2'.
X = 0.5

Simplifying
X = 0.5
Subproblem 2
Set the factor '(1 + -2X)' equal to zero and attempt to solve:

Simplifying
1 + -2X = 0

Solving
1 + -2X = 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 + -2X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2X = 0 + -1
-2X = 0 + -1

Combine like terms: 0 + -1 = -1
-2X = -1

Divide each side by '-2'.
X = 0.5

Simplifying
X = 0.5
Solution
X = {0.5, 0.5}