18t^2+45t=500

Solution for 18t^2+45t=500 equation:

Simplifying
18t2 + 45t = 500

Reorder the terms:
45t + 18t2 = 500

Solving
45t + 18t2 = 500

Solving for variable 't'.

Reorder the terms:
-500 + 45t + 18t2 = 500 + -500

Combine like terms: 500 + -500 = 0
-500 + 45t + 18t2 = 0

Factor a trinomial.
(-20 + -3t)(25 + -6t) = 0

Subproblem 1
Set the factor '(-20 + -3t)' equal to zero and attempt to solve:

Simplifying
-20 + -3t = 0

Solving
-20 + -3t = 0

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

Add '20' to each side of the equation.
-20 + 20 + -3t = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3t = 0 + 20
-3t = 0 + 20

Combine like terms: 0 + 20 = 20
-3t = 20

Divide each side by '-3'.
t = -6.666666667

Simplifying
t = -6.666666667
Subproblem 2
Set the factor '(25 + -6t)' equal to zero and attempt to solve:

Simplifying
25 + -6t = 0

Solving
25 + -6t = 0

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

Add '-25' to each side of the equation.
25 + -25 + -6t = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -6t = 0 + -25
-6t = 0 + -25

Combine like terms: 0 + -25 = -25
-6t = -25

Divide each side by '-6'.
t = 4.166666667

Simplifying
t = 4.166666667
Solution
t = {-6.666666667, 4.166666667}