0=2-2x-24x^2

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Solution for 0=2-2x-24x^2 equation: 


Simplifying
0 = 2 + -2x + -24x2

Solving
0 = 2 + -2x + -24x2

Solving for variable 'x'.

Combine like terms: 0 + -2 = -2
-2 + 2x + 24x2 = 2 + -2x + -24x2 + -2 + 2x + 24x2

Reorder the terms:
-2 + 2x + 24x2 = 2 + -2 + -2x + 2x + -24x2 + 24x2

Combine like terms: 2 + -2 = 0
-2 + 2x + 24x2 = 0 + -2x + 2x + -24x2 + 24x2
-2 + 2x + 24x2 = -2x + 2x + -24x2 + 24x2

Combine like terms: -2x + 2x = 0
-2 + 2x + 24x2 = 0 + -24x2 + 24x2
-2 + 2x + 24x2 = -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
-2 + 2x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + x + 12x2) = 0

Factor a trinomial.
2((-1 + -3x)(1 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-0.3333333333, 0.25}

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