10t^2-9t=1

Solution for 10t^2-9t=1 equation:

Simplifying
10t2 + -9t = 1

Reorder the terms:
-9t + 10t2 = 1

Solving
-9t + 10t2 = 1

Solving for variable 't'.

Reorder the terms:
-1 + -9t + 10t2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -9t + 10t2 = 0

Factor a trinomial.
(-1 + -10t)(1 + -1t) = 0

Subproblem 1
Set the factor '(-1 + -10t)' equal to zero and attempt to solve:

Simplifying
-1 + -10t = 0

Solving
-1 + -10t = 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 + -10t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -10t = 0 + 1
-10t = 0 + 1

Combine like terms: 0 + 1 = 1
-10t = 1

Divide each side by '-10'.
t = -0.1

Simplifying
t = -0.1
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 = {-0.1, 1}