3t(t-4)=15

Solution for 3t(t-4)=15 equation:

Simplifying
3t(t + -4) = 15

Reorder the terms:
3t(-4 + t) = 15
(-4 * 3t + t * 3t) = 15
(-12t + 3t2) = 15

Solving
-12t + 3t2 = 15

Solving for variable 't'.

Reorder the terms:
-15 + -12t + 3t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -12t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4t + t2) = 0

Factor a trinomial.
3((-1 + -1t)(5 + -1t)) = 0

Ignore the factor 3.
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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-1, 5}