8a^2-88a+224=0

Solution for 8a^2-88a+224=0 equation:

Simplifying
8a2 + -88a + 224 = 0

Reorder the terms:
224 + -88a + 8a2 = 0

Solving
224 + -88a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(28 + -11a + a2) = 0

Factor a trinomial.
8((4 + -1a)(7 + -1a)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

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

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

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {4, 7}