-4k^2+8k+1=5

Solution for -4k^2+8k+1=5 equation:

Simplifying
-4k2 + 8k + 1 = 5

Reorder the terms:
1 + 8k + -4k2 = 5

Solving
1 + 8k + -4k2 = 5

Solving for variable 'k'.

Reorder the terms:
1 + -5 + 8k + -4k2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + 8k + -4k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + 8k + -4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 2k + -1k2) = 0

Factor a trinomial.
4((-1 + k)(1 + -1k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + k)' equal to zero and attempt to solve:

Simplifying
-1 + k = 0

Solving
-1 + k = 0

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

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

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

Combine like terms: 0 + 1 = 1
k = 1

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {1, 1}