45=a(a+4)

Solution for 45=a(a+4) equation:

Simplifying
45 = a(a + 4)

Reorder the terms:
45 = a(4 + a)
45 = (4 * a + a * a)
45 = (4a + a2)

Solving
45 = 4a + a2

Solving for variable 'a'.

Reorder the terms:
45 + -4a + -1a2 = 4a + -4a + a2 + -1a2

Combine like terms: 4a + -4a = 0
45 + -4a + -1a2 = 0 + a2 + -1a2
45 + -4a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
45 + -4a + -1a2 = 0

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

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

Simplifying
9 + a = 0

Solving
9 + a = 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 + a = 0 + -9

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

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

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