(6a^2+5a)(-12a+2)=0

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Solution for (6a^2+5a)(-12a+2)=0 equation: 


Simplifying
(6a2 + 5a)(-12a + 2) = 0

Reorder the terms:
(5a + 6a2)(-12a + 2) = 0

Reorder the terms:
(5a + 6a2)(2 + -12a) = 0

Multiply (5a + 6a2) * (2 + -12a)
(5a * (2 + -12a) + 6a2 * (2 + -12a)) = 0
((2 * 5a + -12a * 5a) + 6a2 * (2 + -12a)) = 0
((10a + -60a2) + 6a2 * (2 + -12a)) = 0
(10a + -60a2 + (2 * 6a2 + -12a * 6a2)) = 0
(10a + -60a2 + (12a2 + -72a3)) = 0

Combine like terms: -60a2 + 12a2 = -48a2
(10a + -48a2 + -72a3) = 0

Solving
10a + -48a2 + -72a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(5 + -24a + -36a2) = 0

Factor a trinomial.
2a((1 + -6a)(5 + 6a)) = 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 + -6a)' equal to zero and attempt to solve:

Simplifying
1 + -6a = 0

Solving
1 + -6a = 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 + -6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6a = 0 + -1
-6a = 0 + -1

Combine like terms: 0 + -1 = -1
-6a = -1

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667

Subproblem 3
Set the factor '(5 + 6a)' equal to zero and attempt to solve:

Simplifying
5 + 6a = 0

Solving
5 + 6a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 6a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6a = 0 + -5
6a = 0 + -5

Combine like terms: 0 + -5 = -5
6a = -5

Divide each side by '6'.
a = -0.8333333333

Simplifying
a = -0.8333333333
Solution
a = {0, 0.1666666667, -0.8333333333}

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