36a^2-160a+96=-8a-4a^2

Solution for 36a^2-160a+96=-8a-4a^2 equation:

Simplifying
36a2 + -160a + 96 = -8a + -4a2

Reorder the terms:
96 + -160a + 36a2 = -8a + -4a2

Solving
96 + -160a + 36a2 = -8a + -4a2

Solving for variable 'a'.

Reorder the terms:
96 + -160a + 8a + 36a2 + 4a2 = -8a + -4a2 + 8a + 4a2

Combine like terms: -160a + 8a = -152a
96 + -152a + 36a2 + 4a2 = -8a + -4a2 + 8a + 4a2

Combine like terms: 36a2 + 4a2 = 40a2
96 + -152a + 40a2 = -8a + -4a2 + 8a + 4a2

Reorder the terms:
96 + -152a + 40a2 = -8a + 8a + -4a2 + 4a2

Combine like terms: -8a + 8a = 0
96 + -152a + 40a2 = 0 + -4a2 + 4a2
96 + -152a + 40a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
96 + -152a + 40a2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(12 + -19a + 5a2) = 0

Factor a trinomial.
8((4 + -5a)(3 + -1a)) = 0

Ignore the factor 8.
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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {0.8, 3}