3a^2=12a+15

Solution for 3a^2=12a+15 equation:

Simplifying
3a2 = 12a + 15

Reorder the terms:
3a2 = 15 + 12a

Solving
3a2 = 15 + 12a

Solving for variable 'a'.

Reorder the terms:
-15 + -12a + 3a2 = 15 + 12a + -15 + -12a

Reorder the terms:
-15 + -12a + 3a2 = 15 + -15 + 12a + -12a

Combine like terms: 15 + -15 = 0
-15 + -12a + 3a2 = 0 + 12a + -12a
-15 + -12a + 3a2 = 12a + -12a

Combine like terms: 12a + -12a = 0
-15 + -12a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4a + a2) = 0

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

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

Simplifying
-1 + -1a = 0

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

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

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

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

Simplifying
a = -1
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 = {-1, 5}