6a^2=a+12

Solution for 6a^2=a+12 equation:

Simplifying
6a2 = a + 12

Reorder the terms:
6a2 = 12 + a

Solving
6a2 = 12 + a

Solving for variable 'a'.

Reorder the terms:
-12 + -1a + 6a2 = 12 + a + -12 + -1a

Reorder the terms:
-12 + -1a + 6a2 = 12 + -12 + a + -1a

Combine like terms: 12 + -12 = 0
-12 + -1a + 6a2 = 0 + a + -1a
-12 + -1a + 6a2 = a + -1a

Combine like terms: a + -1a = 0
-12 + -1a + 6a2 = 0

Factor a trinomial.
(-4 + -3a)(3 + -2a) = 0

Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve:

Simplifying
-4 + -3a = 0

Solving
-4 + -3a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3a = 0 + 4
-3a = 0 + 4

Combine like terms: 0 + 4 = 4
-3a = 4

Divide each side by '-3'.
a = -1.333333333

Simplifying
a = -1.333333333
Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-1.333333333, 1.5}