4s^2+4s+1=1+6s

Solution for 4s^2+4s+1=1+6s equation:

Simplifying
4s2 + 4s + 1 = 1 + 6s

Reorder the terms:
1 + 4s + 4s2 = 1 + 6s

Add '-1' to each side of the equation.
1 + 4s + -1 + 4s2 = 1 + -1 + 6s

Reorder the terms:
1 + -1 + 4s + 4s2 = 1 + -1 + 6s

Combine like terms: 1 + -1 = 0
0 + 4s + 4s2 = 1 + -1 + 6s
4s + 4s2 = 1 + -1 + 6s

Combine like terms: 1 + -1 = 0
4s + 4s2 = 0 + 6s
4s + 4s2 = 6s

Solving
4s + 4s2 = 6s

Solving for variable 's'.

Reorder the terms:
4s + -6s + 4s2 = 6s + -6s

Combine like terms: 4s + -6s = -2s
-2s + 4s2 = 6s + -6s

Combine like terms: 6s + -6s = 0
-2s + 4s2 = 0

Factor out the Greatest Common Factor (GCF), '2s'.
2s(-1 + 2s) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(-1 + 2s)' equal to zero and attempt to solve:

Simplifying
-1 + 2s = 0

Solving
-1 + 2s = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2s = 0 + 1
2s = 0 + 1

Combine like terms: 0 + 1 = 1
2s = 1

Divide each side by '2'.
s = 0.5

Simplifying
s = 0.5
Solution
s = {0, 0.5}