10t^2+t=9

Solution for 10t^2+t=9 equation:

Simplifying
10t2 + t = 9

Reorder the terms:
t + 10t2 = 9

Solving
t + 10t2 = 9

Solving for variable 't'.

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

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

Factor a trinomial.
(-1 + -1t)(9 + -10t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -10t)' equal to zero and attempt to solve:

Simplifying
9 + -10t = 0

Solving
9 + -10t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -10t = 0 + -9

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

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

Divide each side by '-10'.
t = 0.9

Simplifying
t = 0.9
Solution
t = {-1, 0.9}