2(a^2+5)=9a

Solution for 2(a^2+5)=9a equation:

Simplifying
2(a2 + 5) = 9a

Reorder the terms:
2(5 + a2) = 9a
(5 * 2 + a2 * 2) = 9a
(10 + 2a2) = 9a

Solving
10 + 2a2 = 9a

Solving for variable 'a'.

Reorder the terms:
10 + -9a + 2a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
10 + -9a + 2a2 = 0

Factor a trinomial.
(2 + -1a)(5 + -2a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 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 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {2, 2.5}