t(10t+30)=180

Solution for t(10t+30)=180 equation:

Simplifying
t(10t + 30) = 180

Reorder the terms:
t(30 + 10t) = 180
(30 * t + 10t * t) = 180
(30t + 10t2) = 180

Solving
30t + 10t2 = 180

Solving for variable 't'.

Reorder the terms:
-180 + 30t + 10t2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 30t + 10t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-18 + 3t + t2) = 0

Factor a trinomial.
10((-6 + -1t)(3 + -1t)) = 0

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
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
Solution
t = {-6, 3}