2(a^2+3)=13a

Solution for 2(a^2+3)=13a equation:

Simplifying
2(a2 + 3) = 13a

Reorder the terms:
2(3 + a2) = 13a
(3 * 2 + a2 * 2) = 13a
(6 + 2a2) = 13a

Solving
6 + 2a2 = 13a

Solving for variable 'a'.

Reorder the terms:
6 + -13a + 2a2 = 13a + -13a

Combine like terms: 13a + -13a = 0
6 + -13a + 2a2 = 0

Factor a trinomial.
(1 + -2a)(6 + -1a) = 0

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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

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

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

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {0.5, 6}