-5a^2+31a=6

Solution for -5a^2+31a=6 equation:

Simplifying
-5a2 + 31a = 6

Reorder the terms:
31a + -5a2 = 6

Solving
31a + -5a2 = 6

Solving for variable 'a'.

Reorder the terms:
-6 + 31a + -5a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 31a + -5a2 = 0

Factor a trinomial.
(-6 + a)(1 + -5a) = 0

Subproblem 1
Set the factor '(-6 + a)' equal to zero and attempt to solve:

Simplifying
-6 + a = 0

Solving
-6 + a = 0

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

Add '6' to each side of the equation.
-6 + 6 + a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + a = 0 + 6
a = 0 + 6

Combine like terms: 0 + 6 = 6
a = 6

Simplifying
a = 6
Subproblem 2
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
Solution
a = {6, 0.2}