20a^2=-6+22a

Solution for 20a^2=-6+22a equation:

Simplifying
20a2 = -6 + 22a

Solving
20a2 = -6 + 22a

Solving for variable 'a'.

Reorder the terms:
6 + -22a + 20a2 = -6 + 22a + 6 + -22a

Reorder the terms:
6 + -22a + 20a2 = -6 + 6 + 22a + -22a

Combine like terms: -6 + 6 = 0
6 + -22a + 20a2 = 0 + 22a + -22a
6 + -22a + 20a2 = 22a + -22a

Combine like terms: 22a + -22a = 0
6 + -22a + 20a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -11a + 10a2) = 0

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

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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

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

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

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Subproblem 2
Set the factor '(3 + -5a)' equal to zero and attempt to solve:

Simplifying
3 + -5a = 0

Solving
3 + -5a = 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 + -5a = 0 + -3

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

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

Divide each side by '-5'.
a = 0.6

Simplifying
a = 0.6
Solution
a = {0.5, 0.6}