(3t-10)(t+2)=0

Solution for (3t-10)(t+2)=0 equation:

Simplifying
(3t + -10)(t + 2) = 0

Reorder the terms:
(-10 + 3t)(t + 2) = 0

Reorder the terms:
(-10 + 3t)(2 + t) = 0

Multiply (-10 + 3t) * (2 + t)
(-10(2 + t) + 3t * (2 + t)) = 0
((2 * -10 + t * -10) + 3t * (2 + t)) = 0
((-20 + -10t) + 3t * (2 + t)) = 0
(-20 + -10t + (2 * 3t + t * 3t)) = 0
(-20 + -10t + (6t + 3t2)) = 0

Combine like terms: -10t + 6t = -4t
(-20 + -4t + 3t2) = 0

Solving
-20 + -4t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-2 + -1t)(10 + -3t) = 0

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(10 + -3t)' equal to zero and attempt to solve:

Simplifying
10 + -3t = 0

Solving
10 + -3t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3t = 0 + -10
-3t = 0 + -10

Combine like terms: 0 + -10 = -10
-3t = -10

Divide each side by '-3'.
t = 3.333333333

Simplifying
t = 3.333333333
Solution
t = {-2, 3.333333333}