(a*a)-15a+56=0

Solution for (a*a)-15a+56=0 equation:

Simplifying
(a * a) + -15a + 56 = 0

Multiply a * a
(a2) + -15a + 56 = 0
a2 + -15a + 56 = 0

Reorder the terms:
56 + -15a + a2 = 0

Solving
56 + -15a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {7, 8}