(t-3)(t-7)=0

Solution for (t-3)(t-7)=0 equation:

Simplifying
(t + -3)(t + -7) = 0

Reorder the terms:
(-3 + t)(t + -7) = 0

Reorder the terms:
(-3 + t)(-7 + t) = 0

Multiply (-3 + t) * (-7 + t)
(-3(-7 + t) + t(-7 + t)) = 0
((-7 * -3 + t * -3) + t(-7 + t)) = 0
((21 + -3t) + t(-7 + t)) = 0
(21 + -3t + (-7 * t + t * t)) = 0
(21 + -3t + (-7t + t2)) = 0

Combine like terms: -3t + -7t = -10t
(21 + -10t + t2) = 0

Solving
21 + -10t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -1t)(7 + -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 '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {3, 7}