(4a+6)(6a^2-3a+1)=0

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Solution for (4a+6)(6a^2-3a+1)=0 equation:


Simplifying
(4a + 6)(6a2 + -3a + 1) = 0

Reorder the terms:
(6 + 4a)(6a2 + -3a + 1) = 0

Reorder the terms:
(6 + 4a)(1 + -3a + 6a2) = 0

Multiply (6 + 4a) * (1 + -3a + 6a2)
(6(1 + -3a + 6a2) + 4a * (1 + -3a + 6a2)) = 0
((1 * 6 + -3a * 6 + 6a2 * 6) + 4a * (1 + -3a + 6a2)) = 0
((6 + -18a + 36a2) + 4a * (1 + -3a + 6a2)) = 0
(6 + -18a + 36a2 + (1 * 4a + -3a * 4a + 6a2 * 4a)) = 0
(6 + -18a + 36a2 + (4a + -12a2 + 24a3)) = 0

Reorder the terms:
(6 + -18a + 4a + 36a2 + -12a2 + 24a3) = 0

Combine like terms: -18a + 4a = -14a
(6 + -14a + 36a2 + -12a2 + 24a3) = 0

Combine like terms: 36a2 + -12a2 = 24a2
(6 + -14a + 24a2 + 24a3) = 0

Solving
6 + -14a + 24a2 + 24a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7a + 12a2 + 12a3) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -7a + 12a2 + 12a3)' equal to zero and attempt to solve: Simplifying 3 + -7a + 12a2 + 12a3 = 0 Solving 3 + -7a + 12a2 + 12a3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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