2(a^2+12)=19a

Solution for 2(a^2+12)=19a equation:

Simplifying
2(a2 + 12) = 19a

Reorder the terms:
2(12 + a2) = 19a
(12 * 2 + a2 * 2) = 19a
(24 + 2a2) = 19a

Solving
24 + 2a2 = 19a

Solving for variable 'a'.

Reorder the terms:
24 + -19a + 2a2 = 19a + -19a

Combine like terms: 19a + -19a = 0
24 + -19a + 2a2 = 0

Factor a trinomial.
(3 + -2a)(8 + -1a) = 0

Subproblem 1
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {1.5, 8}