(18t^2)+(53t)-3=0

Solution for (18t^2)+(53t)-3=0 equation:

Simplifying
(18t2) + (53t) + -3 = 0

Reorder the terms:
-3 + (53t) + (18t2) = 0

Solving
-3 + (53t) + (18t2) = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(1 + -18t) = 0

Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve:

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
Subproblem 2
Set the factor '(1 + -18t)' equal to zero and attempt to solve:

Simplifying
1 + -18t = 0

Solving
1 + -18t = 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 + -18t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -18t = 0 + -1
-18t = 0 + -1

Combine like terms: 0 + -1 = -1
-18t = -1

Divide each side by '-18'.
t = 0.05555555556

Simplifying
t = 0.05555555556
Solution
t = {-3, 0.05555555556}