2(a^2+15)=23a

Solution for 2(a^2+15)=23a equation:

Simplifying
2(a2 + 15) = 23a

Reorder the terms:
2(15 + a2) = 23a
(15 * 2 + a2 * 2) = 23a
(30 + 2a2) = 23a

Solving
30 + 2a2 = 23a

Solving for variable 'a'.

Reorder the terms:
30 + -23a + 2a2 = 23a + -23a

Combine like terms: 23a + -23a = 0
30 + -23a + 2a2 = 0

Factor a trinomial.
(3 + -2a)(10 + -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 '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Solution
a = {1.5, 10}