6=a^2-5a

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

Simplifying
6 = a2 + -5a

Reorder the terms:
6 = -5a + a2

Solving
6 = -5a + a2

Solving for variable 'a'.

Reorder the terms:
6 + 5a + -1a2 = -5a + 5a + a2 + -1a2

Combine like terms: -5a + 5a = 0
6 + 5a + -1a2 = 0 + a2 + -1a2
6 + 5a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
6 + 5a + -1a2 = 0

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

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

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
Solution
a = {6, -1}