(t-3)(t-4)=0

Solution for (t-3)(t-4)=0 equation:

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

Reorder the terms:
(-3 + t)(t + -4) = 0

Reorder the terms:
(-3 + t)(-4 + t) = 0

Multiply (-3 + t) * (-4 + t)
(-3(-4 + t) + t(-4 + t)) = 0
((-4 * -3 + t * -3) + t(-4 + t)) = 0
((12 + -3t) + t(-4 + t)) = 0
(12 + -3t + (-4 * t + t * t)) = 0
(12 + -3t + (-4t + t2)) = 0

Combine like terms: -3t + -4t = -7t
(12 + -7t + t2) = 0

Solving
12 + -7t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
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 = {3, 4}