(t+7)(t-2)=

Solution for (t+7)(t-2)= equation:

Simplifying
(t + 7)(t + -2) = 0

Reorder the terms:
(7 + t)(t + -2) = 0

Reorder the terms:
(7 + t)(-2 + t) = 0

Multiply (7 + t) * (-2 + t)
(7(-2 + t) + t(-2 + t)) = 0
((-2 * 7 + t * 7) + t(-2 + t)) = 0
((-14 + 7t) + t(-2 + t)) = 0
(-14 + 7t + (-2 * t + t * t)) = 0
(-14 + 7t + (-2t + t2)) = 0

Combine like terms: 7t + -2t = 5t
(-14 + 5t + t2) = 0

Solving
-14 + 5t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -1t)(2 + -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 '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-7, 2}