12a^2=45+51a

Solution for 12a^2=45+51a equation:

Simplifying
12a2 = 45 + 51a

Solving
12a2 = 45 + 51a

Solving for variable 'a'.

Reorder the terms:
-45 + -51a + 12a2 = 45 + 51a + -45 + -51a

Reorder the terms:
-45 + -51a + 12a2 = 45 + -45 + 51a + -51a

Combine like terms: 45 + -45 = 0
-45 + -51a + 12a2 = 0 + 51a + -51a
-45 + -51a + 12a2 = 51a + -51a

Combine like terms: 51a + -51a = 0
-45 + -51a + 12a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -17a + 4a2) = 0

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

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

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 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 + -4a = 0 + 3

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

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

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-0.75, 5}