a^2=20a-75

Solution for a^2=20a-75 equation:

Simplifying
a2 = 20a + -75

Reorder the terms:
a2 = -75 + 20a

Solving
a2 = -75 + 20a

Solving for variable 'a'.

Reorder the terms:
75 + -20a + a2 = -75 + 20a + 75 + -20a

Reorder the terms:
75 + -20a + a2 = -75 + 75 + 20a + -20a

Combine like terms: -75 + 75 = 0
75 + -20a + a2 = 0 + 20a + -20a
75 + -20a + a2 = 20a + -20a

Combine like terms: 20a + -20a = 0
75 + -20a + a2 = 0

Factor a trinomial.
(5 + -1a)(15 + -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 '(15 + -1a)' equal to zero and attempt to solve:

Simplifying
15 + -1a = 0

Solving
15 + -1a = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1a = 0 + -15
-1a = 0 + -15

Combine like terms: 0 + -15 = -15
-1a = -15

Divide each side by '-1'.
a = 15

Simplifying
a = 15
Solution
a = {5, 15}