8q^2-7q-1=0

Solution for 8q^2-7q-1=0 equation:

Simplifying
8q2 + -7q + -1 = 0

Reorder the terms:
-1 + -7q + 8q2 = 0

Solving
-1 + -7q + 8q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-1 + -8q = 0

Solving
-1 + -8q = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8q = 0 + 1

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

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

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

Simplifying
q = -0.125
Subproblem 2
Set the factor '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

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