0=-6x^3+26x^2-28x

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Solution for 0=-6x^3+26x^2-28x equation: 


Simplifying
0 = -6x3 + 26x2 + -28x

Reorder the terms:
0 = -28x + 26x2 + -6x3

Solving
0 = -28x + 26x2 + -6x3

Solving for variable 'x'.
Remove the zero:
28x + -26x2 + 6x3 = -28x + 26x2 + -6x3 + 28x + -26x2 + 6x3

Reorder the terms:
28x + -26x2 + 6x3 = -28x + 28x + 26x2 + -26x2 + -6x3 + 6x3

Combine like terms: -28x + 28x = 0
28x + -26x2 + 6x3 = 0 + 26x2 + -26x2 + -6x3 + 6x3
28x + -26x2 + 6x3 = 26x2 + -26x2 + -6x3 + 6x3

Combine like terms: 26x2 + -26x2 = 0
28x + -26x2 + 6x3 = 0 + -6x3 + 6x3
28x + -26x2 + 6x3 = -6x3 + 6x3

Combine like terms: -6x3 + 6x3 = 0
28x + -26x2 + 6x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(14 + -13x + 3x2) = 0

Factor a trinomial.
2x((2 + -1x)(7 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, 2, 2.333333333}

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