6a^2=8a+5a^2-15

Solution for 6a^2=8a+5a^2-15 equation:

Simplifying
6a2 = 8a + 5a2 + -15

Reorder the terms:
6a2 = -15 + 8a + 5a2

Solving
6a2 = -15 + 8a + 5a2

Solving for variable 'a'.

Reorder the terms:
15 + -8a + 6a2 + -5a2 = -15 + 8a + 5a2 + 15 + -8a + -5a2

Combine like terms: 6a2 + -5a2 = 1a2
15 + -8a + 1a2 = -15 + 8a + 5a2 + 15 + -8a + -5a2

Reorder the terms:
15 + -8a + 1a2 = -15 + 15 + 8a + -8a + 5a2 + -5a2

Combine like terms: -15 + 15 = 0
15 + -8a + 1a2 = 0 + 8a + -8a + 5a2 + -5a2
15 + -8a + 1a2 = 8a + -8a + 5a2 + -5a2

Combine like terms: 8a + -8a = 0
15 + -8a + 1a2 = 0 + 5a2 + -5a2
15 + -8a + 1a2 = 5a2 + -5a2

Combine like terms: 5a2 + -5a2 = 0
15 + -8a + 1a2 = 0

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

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
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 = {3, 5}