2(a^2+2)=9a

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

Simplifying
2(a2 + 2) = 9a

Reorder the terms:
2(2 + a2) = 9a
(2 * 2 + a2 * 2) = 9a
(4 + 2a2) = 9a

Solving
4 + 2a2 = 9a

Solving for variable 'a'.

Reorder the terms:
4 + -9a + 2a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
4 + -9a + 2a2 = 0

Factor a trinomial.
(1 + -2a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {0.5, 4}