(a^2)=45-4a

Solution for (a^2)=45-4a equation:

Simplifying
(a2) = 45 + -4a
a2 = 45 + -4a

Solving
a2 = 45 + -4a

Solving for variable 'a'.

Reorder the terms:
-45 + 4a + a2 = 45 + -4a + -45 + 4a

Reorder the terms:
-45 + 4a + a2 = 45 + -45 + -4a + 4a

Combine like terms: 45 + -45 = 0
-45 + 4a + a2 = 0 + -4a + 4a
-45 + 4a + a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
-45 + 4a + a2 = 0

Factor a trinomial.
(-9 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-9, 5}