a(2a-8)=330

Solution for a(2a-8)=330 equation:

Simplifying
a(2a + -8) = 330

Reorder the terms:
a(-8 + 2a) = 330
(-8 * a + 2a * a) = 330
(-8a + 2a2) = 330

Solving
-8a + 2a2 = 330

Solving for variable 'a'.

Reorder the terms:
-330 + -8a + 2a2 = 330 + -330

Combine like terms: 330 + -330 = 0
-330 + -8a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-165 + -4a + a2) = 0

Factor a trinomial.
2((-11 + -1a)(15 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -1a)' equal to zero and attempt to solve:

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
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 = {-11, 15}