6a^3-12a^2+14a=0

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Solution for 6a^3-12a^2+14a=0 equation:


Simplifying
6a3 + -12a2 + 14a = 0

Reorder the terms:
14a + -12a2 + 6a3 = 0

Solving
14a + -12a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(7 + -6a + 3a2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(7 + -6a + 3a2)' equal to zero and attempt to solve: Simplifying 7 + -6a + 3a2 = 0 Solving 7 + -6a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -2a + a2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -2a + -2.333333333 + a2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -2a + a2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -2a + a2 = 0 + -2.333333333 -2a + a2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -2a + a2 = -2.333333333 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = -2.333333333 + 1 Reorder the terms: 1 + -2a + a2 = -2.333333333 + 1 Combine like terms: -2.333333333 + 1 = -1.333333333 1 + -2a + a2 = -1.333333333 Factor a perfect square on the left side: (a + -1)(a + -1) = -1.333333333 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

a = {0}

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