6(4x^2+1)=24x

Solution for 6(4x^2+1)=24x equation:

Simplifying
6(4x2 + 1) = 24x

Reorder the terms:
6(1 + 4x2) = 24x
(1 * 6 + 4x2 * 6) = 24x
(6 + 24x2) = 24x

Solving
6 + 24x2 = 24x

Solving for variable 'x'.

Reorder the terms:
6 + -24x + 24x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
6 + -24x + 24x2 = 0

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}