2(3a^2-1)-6a=5a

Solution for 2(3a^2-1)-6a=5a equation:

Simplifying
2(3a2 + -1) + -6a = 5a

Reorder the terms:
2(-1 + 3a2) + -6a = 5a
(-1 * 2 + 3a2 * 2) + -6a = 5a
(-2 + 6a2) + -6a = 5a

Reorder the terms:
-2 + -6a + 6a2 = 5a

Solving
-2 + -6a + 6a2 = 5a

Solving for variable 'a'.

Reorder the terms:
-2 + -6a + -5a + 6a2 = 5a + -5a

Combine like terms: -6a + -5a = -11a
-2 + -11a + 6a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-2 + -11a + 6a2 = 0

Factor a trinomial.
(-1 + -6a)(2 + -1a) = 0

Subproblem 1
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 2
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 = {-0.1666666667, 2}