0=-6x^2+2x+4

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Solution for 0=-6x^2+2x+4 equation: 


Simplifying
0 = -6x2 + 2x + 4

Reorder the terms:
0 = 4 + 2x + -6x2

Solving
0 = 4 + 2x + -6x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -2x + 6x2 = 4 + 2x + -6x2 + -4 + -2x + 6x2

Reorder the terms:
-4 + -2x + 6x2 = 4 + -4 + 2x + -2x + -6x2 + 6x2

Combine like terms: 4 + -4 = 0
-4 + -2x + 6x2 = 0 + 2x + -2x + -6x2 + 6x2
-4 + -2x + 6x2 = 2x + -2x + -6x2 + 6x2

Combine like terms: 2x + -2x = 0
-4 + -2x + 6x2 = 0 + -6x2 + 6x2
-4 + -2x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4 + -2x + 6x2 = 0

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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
Solution
x = {-0.6666666667, 1}

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