a^2+8a-20=6a-5a^2

Solution for a^2+8a-20=6a-5a^2 equation:

Simplifying
a2 + 8a + -20 = 6a + -5a2

Reorder the terms:
-20 + 8a + a2 = 6a + -5a2

Solving
-20 + 8a + a2 = 6a + -5a2

Solving for variable 'a'.

Reorder the terms:
-20 + 8a + -6a + a2 + 5a2 = 6a + -5a2 + -6a + 5a2

Combine like terms: 8a + -6a = 2a
-20 + 2a + a2 + 5a2 = 6a + -5a2 + -6a + 5a2

Combine like terms: a2 + 5a2 = 6a2
-20 + 2a + 6a2 = 6a + -5a2 + -6a + 5a2

Reorder the terms:
-20 + 2a + 6a2 = 6a + -6a + -5a2 + 5a2

Combine like terms: 6a + -6a = 0
-20 + 2a + 6a2 = 0 + -5a2 + 5a2
-20 + 2a + 6a2 = -5a2 + 5a2

Combine like terms: -5a2 + 5a2 = 0
-20 + 2a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + a + 3a2) = 0

Factor a trinomial.
2((-2 + -1a)(5 + -3a)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-2, 1.666666667}