2a(a-1)(3a-1)=0

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Solution for 2a(a-1)(3a-1)=0 equation:


Simplifying
2a(a + -1)(3a + -1) = 0

Reorder the terms:
2a(-1 + a)(3a + -1) = 0

Reorder the terms:
2a(-1 + a)(-1 + 3a) = 0

Multiply (-1 + a) * (-1 + 3a)
2a(-1(-1 + 3a) + a(-1 + 3a)) = 0
2a((-1 * -1 + 3a * -1) + a(-1 + 3a)) = 0
2a((1 + -3a) + a(-1 + 3a)) = 0
2a(1 + -3a + (-1 * a + 3a * a)) = 0
2a(1 + -3a + (-1a + 3a2)) = 0

Combine like terms: -3a + -1a = -4a
2a(1 + -4a + 3a2) = 0
(1 * 2a + -4a * 2a + 3a2 * 2a) = 0
(2a + -8a2 + 6a3) = 0

Solving
2a + -8a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(1 + -4a + 3a2) = 0

Factor a trinomial.
2a((1 + -3a)(1 + -1a)) = 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 '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333

Subproblem 3

Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1

Solution

a = {0, 0.3333333333, 1}

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