25a^2-178a+120=-8a

Solution for 25a^2-178a+120=-8a equation:

Simplifying
25a2 + -178a + 120 = -8a

Reorder the terms:
120 + -178a + 25a2 = -8a

Solving
120 + -178a + 25a2 = -8a

Solving for variable 'a'.

Reorder the terms:
120 + -178a + 8a + 25a2 = -8a + 8a

Combine like terms: -178a + 8a = -170a
120 + -170a + 25a2 = -8a + 8a

Combine like terms: -8a + 8a = 0
120 + -170a + 25a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + -34a + 5a2) = 0

Factor a trinomial.
5((4 + -5a)(6 + -1a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(4 + -5a)' equal to zero and attempt to solve:

Simplifying
4 + -5a = 0

Solving
4 + -5a = 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 + -5a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5a = 0 + -4
-5a = 0 + -4

Combine like terms: 0 + -4 = -4
-5a = -4

Divide each side by '-5'.
a = 0.8

Simplifying
a = 0.8
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {0.8, 6}