52=8a^2+10a

Solution for 52=8a^2+10a equation:

Simplifying
52 = 8a2 + 10a

Reorder the terms:
52 = 10a + 8a2

Solving
52 = 10a + 8a2

Solving for variable 'a'.

Reorder the terms:
52 + -10a + -8a2 = 10a + -10a + 8a2 + -8a2

Combine like terms: 10a + -10a = 0
52 + -10a + -8a2 = 0 + 8a2 + -8a2
52 + -10a + -8a2 = 8a2 + -8a2

Combine like terms: 8a2 + -8a2 = 0
52 + -10a + -8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(26 + -5a + -4a2) = 0

Factor a trinomial.
2((2 + -1a)(13 + 4a)) = 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 '(13 + 4a)' equal to zero and attempt to solve:

Simplifying
13 + 4a = 0

Solving
13 + 4a = 0

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

Add '-13' to each side of the equation.
13 + -13 + 4a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 4a = 0 + -13
4a = 0 + -13

Combine like terms: 0 + -13 = -13
4a = -13

Divide each side by '4'.
a = -3.25

Simplifying
a = -3.25
Solution
a = {2, -3.25}