5a(3a-1)(2a-4)=0

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Solution for 5a(3a-1)(2a-4)=0 equation:


Simplifying
5a(3a + -1)(2a + -4) = 0

Reorder the terms:
5a(-1 + 3a)(2a + -4) = 0

Reorder the terms:
5a(-1 + 3a)(-4 + 2a) = 0

Multiply (-1 + 3a) * (-4 + 2a)
5a(-1(-4 + 2a) + 3a * (-4 + 2a)) = 0
5a((-4 * -1 + 2a * -1) + 3a * (-4 + 2a)) = 0
5a((4 + -2a) + 3a * (-4 + 2a)) = 0
5a(4 + -2a + (-4 * 3a + 2a * 3a)) = 0
5a(4 + -2a + (-12a + 6a2)) = 0

Combine like terms: -2a + -12a = -14a
5a(4 + -14a + 6a2) = 0
(4 * 5a + -14a * 5a + 6a2 * 5a) = 0
(20a + -70a2 + 30a3) = 0

Solving
20a + -70a2 + 30a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10a'.
10a(2 + -7a + 3a2) = 0

Factor a trinomial.
10a((1 + -3a)(2 + -1a)) = 0

Ignore the factor 10.

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

Solution

a = {0, 0.3333333333, 2}

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