2t(t-4)+3(t-4)=

Solution for 2t(t-4)+3(t-4)= equation:

Simplifying
2t(t + -4) + 3(t + -4) = 0

Reorder the terms:
2t(-4 + t) + 3(t + -4) = 0
(-4 * 2t + t * 2t) + 3(t + -4) = 0
(-8t + 2t2) + 3(t + -4) = 0

Reorder the terms:
-8t + 2t2 + 3(-4 + t) = 0
-8t + 2t2 + (-4 * 3 + t * 3) = 0
-8t + 2t2 + (-12 + 3t) = 0

Reorder the terms:
-12 + -8t + 3t + 2t2 = 0

Combine like terms: -8t + 3t = -5t
-12 + -5t + 2t2 = 0

Solving
-12 + -5t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -2t)(4 + -1t) = 0

Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve:

Simplifying
-3 + -2t = 0

Solving
-3 + -2t = 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 + -2t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2t = 0 + 3
-2t = 0 + 3

Combine like terms: 0 + 3 = 3
-2t = 3

Divide each side by '-2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 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 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1.5, 4}