8k^2+7k=1

Solution for 8k^2+7k=1 equation:

Simplifying
8k2 + 7k = 1

Reorder the terms:
7k + 8k2 = 1

Solving
7k + 8k2 = 1

Solving for variable 'k'.

Reorder the terms:
-1 + 7k + 8k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 7k + 8k2 = 0

Factor a trinomial.
(-1 + -1k)(1 + -8k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -8k)' equal to zero and attempt to solve:

Simplifying
1 + -8k = 0

Solving
1 + -8k = 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 + -8k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8k = 0 + -1
-8k = 0 + -1

Combine like terms: 0 + -1 = -1
-8k = -1

Divide each side by '-8'.
k = 0.125

Simplifying
k = 0.125
Solution
k = {-1, 0.125}