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

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

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

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

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

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

Combine like terms: 7t + -3t = 4t
(-21 + 4t + t2) = 0

Solving
-21 + 4t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -1t)(3 + -1t) = 0

Subproblem 1
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
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 = {-7, 3}