43t^2-42t-1=0

Solution for 43t^2-42t-1=0 equation:

Simplifying
43t2 + -42t + -1 = 0

Reorder the terms:
-1 + -42t + 43t2 = 0

Solving
-1 + -42t + 43t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -43t)(1 + -1t) = 0

Subproblem 1
Set the factor '(-1 + -43t)' equal to zero and attempt to solve:

Simplifying
-1 + -43t = 0

Solving
-1 + -43t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -43t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -43t = 0 + 1
-43t = 0 + 1

Combine like terms: 0 + 1 = 1
-43t = 1

Divide each side by '-43'.
t = -0.02325581395

Simplifying
t = -0.02325581395
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {-0.02325581395, 1}