(3t+1)(t-2)=10

Solution for (3t+1)(t-2)=10 equation:

Simplifying
(3t + 1)(t + -2) = 10

Reorder the terms:
(1 + 3t)(t + -2) = 10

Reorder the terms:
(1 + 3t)(-2 + t) = 10

Multiply (1 + 3t) * (-2 + t)
(1(-2 + t) + 3t * (-2 + t)) = 10
((-2 * 1 + t * 1) + 3t * (-2 + t)) = 10
((-2 + 1t) + 3t * (-2 + t)) = 10
(-2 + 1t + (-2 * 3t + t * 3t)) = 10
(-2 + 1t + (-6t + 3t2)) = 10

Combine like terms: 1t + -6t = -5t
(-2 + -5t + 3t2) = 10

Solving
-2 + -5t + 3t2 = 10

Solving for variable 't'.

Reorder the terms:
-2 + -10 + -5t + 3t2 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + -5t + 3t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + -5t + 3t2 = 0

Factor a trinomial.
(-4 + -3t)(3 + -1t) = 0

Subproblem 1
Set the factor '(-4 + -3t)' equal to zero and attempt to solve:

Simplifying
-4 + -3t = 0

Solving
-4 + -3t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3t = 0 + 4
-3t = 0 + 4

Combine like terms: 0 + 4 = 4
-3t = 4

Divide each side by '-3'.
t = -1.333333333

Simplifying
t = -1.333333333
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 = {-1.333333333, 3}