12a^2=11a+5

Solution for 12a^2=11a+5 equation:

Simplifying
12a2 = 11a + 5

Reorder the terms:
12a2 = 5 + 11a

Solving
12a2 = 5 + 11a

Solving for variable 'a'.

Reorder the terms:
-5 + -11a + 12a2 = 5 + 11a + -5 + -11a

Reorder the terms:
-5 + -11a + 12a2 = 5 + -5 + 11a + -11a

Combine like terms: 5 + -5 = 0
-5 + -11a + 12a2 = 0 + 11a + -11a
-5 + -11a + 12a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
-5 + -11a + 12a2 = 0

Factor a trinomial.
(-1 + -3a)(5 + -4a) = 0

Subproblem 1
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 2
Set the factor '(5 + -4a)' equal to zero and attempt to solve:

Simplifying
5 + -4a = 0

Solving
5 + -4a = 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 + -4a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4a = 0 + -5
-4a = 0 + -5

Combine like terms: 0 + -5 = -5
-4a = -5

Divide each side by '-4'.
a = 1.25

Simplifying
a = 1.25
Solution
a = {-0.3333333333, 1.25}