5a^2-30a-43=-8

Solution for 5a^2-30a-43=-8 equation:

Simplifying
5a2 + -30a + -43 = -8

Reorder the terms:
-43 + -30a + 5a2 = -8

Solving
-43 + -30a + 5a2 = -8

Solving for variable 'a'.

Reorder the terms:
-43 + 8 + -30a + 5a2 = -8 + 8

Combine like terms: -43 + 8 = -35
-35 + -30a + 5a2 = -8 + 8

Combine like terms: -8 + 8 = 0
-35 + -30a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -6a + a2) = 0

Factor a trinomial.
5((-1 + -1a)(7 + -1a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + -1a)' equal to zero and attempt to solve:

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
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 = {-1, 7}