20a^2=52a-32

Solution for 20a^2=52a-32 equation:

Simplifying
20a2 = 52a + -32

Reorder the terms:
20a2 = -32 + 52a

Solving
20a2 = -32 + 52a

Solving for variable 'a'.

Reorder the terms:
32 + -52a + 20a2 = -32 + 52a + 32 + -52a

Reorder the terms:
32 + -52a + 20a2 = -32 + 32 + 52a + -52a

Combine like terms: -32 + 32 = 0
32 + -52a + 20a2 = 0 + 52a + -52a
32 + -52a + 20a2 = 52a + -52a

Combine like terms: 52a + -52a = 0
32 + -52a + 20a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -13a + 5a2) = 0

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

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

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Subproblem 2
Set the factor '(8 + -5a)' equal to zero and attempt to solve:

Simplifying
8 + -5a = 0

Solving
8 + -5a = 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 + -5a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5a = 0 + -8
-5a = 0 + -8

Combine like terms: 0 + -8 = -8
-5a = -8

Divide each side by '-5'.
a = 1.6

Simplifying
a = 1.6
Solution
a = {1, 1.6}