5a^2-2a+6=6-a

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

Simplifying
5a2 + -2a + 6 = 6 + -1a

Reorder the terms:
6 + -2a + 5a2 = 6 + -1a

Add '-6' to each side of the equation.
6 + -2a + -6 + 5a2 = 6 + -6 + -1a

Reorder the terms:
6 + -6 + -2a + 5a2 = 6 + -6 + -1a

Combine like terms: 6 + -6 = 0
0 + -2a + 5a2 = 6 + -6 + -1a
-2a + 5a2 = 6 + -6 + -1a

Combine like terms: 6 + -6 = 0
-2a + 5a2 = 0 + -1a
-2a + 5a2 = -1a

Solving
-2a + 5a2 = -1a

Solving for variable 'a'.

Reorder the terms:
-2a + a + 5a2 = -1a + a

Combine like terms: -2a + a = -1a
-1a + 5a2 = -1a + a

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + 5a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
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 = {0, 0.2}