a(a-4)=45

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

Simplifying
a(a + -4) = 45

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

Solving
-4a + a2 = 45

Solving for variable 'a'.

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

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

Factor a trinomial.
(-5 + -1a)(9 + -1a) = 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 + -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
Solution
a = {-5, 9}