8a^2=-40a+112

Solution for 8a^2=-40a+112 equation:

Simplifying
8a2 = -40a + 112

Reorder the terms:
8a2 = 112 + -40a

Solving
8a2 = 112 + -40a

Solving for variable 'a'.

Reorder the terms:
-112 + 40a + 8a2 = 112 + -40a + -112 + 40a

Reorder the terms:
-112 + 40a + 8a2 = 112 + -112 + -40a + 40a

Combine like terms: 112 + -112 = 0
-112 + 40a + 8a2 = 0 + -40a + 40a
-112 + 40a + 8a2 = -40a + 40a

Combine like terms: -40a + 40a = 0
-112 + 40a + 8a2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-14 + 5a + a2) = 0

Factor a trinomial.
8((-7 + -1a)(2 + -1a)) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-7, 2}