(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 = -1t
(-12 + -1t + t2) = 0

Solving
-12 + -1t + 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}