2X(6X-7)(3X+1)=0

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Solution for 2X(6X-7)(3X+1)=0 equation: 


Simplifying
2X(6X + -7)(3X + 1) = 0

Reorder the terms:
2X(-7 + 6X)(3X + 1) = 0

Reorder the terms:
2X(-7 + 6X)(1 + 3X) = 0

Multiply (-7 + 6X) * (1 + 3X)
2X(-7(1 + 3X) + 6X * (1 + 3X)) = 0
2X((1 * -7 + 3X * -7) + 6X * (1 + 3X)) = 0
2X((-7 + -21X) + 6X * (1 + 3X)) = 0
2X(-7 + -21X + (1 * 6X + 3X * 6X)) = 0
2X(-7 + -21X + (6X + 18X2)) = 0

Combine like terms: -21X + 6X = -15X
2X(-7 + -15X + 18X2) = 0
(-7 * 2X + -15X * 2X + 18X2 * 2X) = 0
(-14X + -30X2 + 36X3) = 0

Solving
-14X + -30X2 + 36X3 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2X'.
2X(-7 + -15X + 18X2) = 0

Factor a trinomial.
2X((-1 + -3X)(7 + -6X)) = 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 '(-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 3
Set the factor '(7 + -6X)' equal to zero and attempt to solve:

Simplifying
7 + -6X = 0

Solving
7 + -6X = 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 + -6X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6X = 0 + -7
-6X = 0 + -7

Combine like terms: 0 + -7 = -7
-6X = -7

Divide each side by '-6'.
X = 1.166666667

Simplifying
X = 1.166666667
Solution
X = {0, -0.3333333333, 1.166666667}

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