(5t-30)(30t-5)=0

Solution for (5t-30)(30t-5)=0 equation:

Simplifying
(5t + -30)(30t + -5) = 0

Reorder the terms:
(-30 + 5t)(30t + -5) = 0

Reorder the terms:
(-30 + 5t)(-5 + 30t) = 0

Multiply (-30 + 5t) * (-5 + 30t)
(-30(-5 + 30t) + 5t * (-5 + 30t)) = 0
((-5 * -30 + 30t * -30) + 5t * (-5 + 30t)) = 0
((150 + -900t) + 5t * (-5 + 30t)) = 0
(150 + -900t + (-5 * 5t + 30t * 5t)) = 0
(150 + -900t + (-25t + 150t2)) = 0

Combine like terms: -900t + -25t = -925t
(150 + -925t + 150t2) = 0

Solving
150 + -925t + 150t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '25'.
25(6 + -37t + 6t2) = 0

Factor a trinomial.
25((1 + -6t)(6 + -1t)) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(1 + -6t)' equal to zero and attempt to solve:

Simplifying
1 + -6t = 0

Solving
1 + -6t = 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 + -6t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6t = 0 + -1
-6t = 0 + -1

Combine like terms: 0 + -1 = -1
-6t = -1

Divide each side by '-6'.
t = 0.1666666667

Simplifying
t = 0.1666666667
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {0.1666666667, 6}