10a^2+6=32a

Solution for 10a^2+6=32a equation:

Simplifying
10a2 + 6 = 32a

Reorder the terms:
6 + 10a2 = 32a

Solving
6 + 10a2 = 32a

Solving for variable 'a'.

Reorder the terms:
6 + -32a + 10a2 = 32a + -32a

Combine like terms: 32a + -32a = 0
6 + -32a + 10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -16a + 5a2) = 0

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

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

Simplifying
1 + -5a = 0

Solving
1 + -5a = 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 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
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 = {0.2, 3}