a^2+1=4a+1

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

Simplifying
a2 + 1 = 4a + 1

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

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

Add '-1' to each side of the equation.
1 + -1 + a2 = 1 + -1 + 4a

Combine like terms: 1 + -1 = 0
0 + a2 = 1 + -1 + 4a
a2 = 1 + -1 + 4a

Combine like terms: 1 + -1 = 0
a2 = 0 + 4a
a2 = 4a

Solving
a2 = 4a

Solving for variable 'a'.

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

Combine like terms: 4a + -4a = 0
-4a + a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-4 + a) = 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 '(-4 + a)' equal to zero and attempt to solve:

Simplifying
-4 + a = 0

Solving
-4 + a = 0

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

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

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

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

Simplifying
a = 4
Solution
a = {0, 4}