2a^2=20a-32

Solution for 2a^2=20a-32 equation:

Simplifying
2a2 = 20a + -32

Reorder the terms:
2a2 = -32 + 20a

Solving
2a2 = -32 + 20a

Solving for variable 'a'.

Reorder the terms:
32 + -20a + 2a2 = -32 + 20a + 32 + -20a

Reorder the terms:
32 + -20a + 2a2 = -32 + 32 + 20a + -20a

Combine like terms: -32 + 32 = 0
32 + -20a + 2a2 = 0 + 20a + -20a
32 + -20a + 2a2 = 20a + -20a

Combine like terms: 20a + -20a = 0
32 + -20a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -10a + a2) = 0

Factor a trinomial.
2((2 + -1a)(8 + -1a)) = 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 '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {2, 8}