a^2+4=6a-1

Solution for a^2+4=6a-1 equation:

Simplifying
a2 + 4 = 6a + -1

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

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

Solving
4 + a2 = -1 + 6a

Solving for variable 'a'.

Reorder the terms:
4 + 1 + -6a + a2 = -1 + 6a + 1 + -6a

Combine like terms: 4 + 1 = 5
5 + -6a + a2 = -1 + 6a + 1 + -6a

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

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

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

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

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

Simplifying
1 + -1a = 0

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

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

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

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

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

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {1, 5}