(t+5)(t+2)=18

Solution for (t+5)(t+2)=18 equation:

Simplifying
(t + 5)(t + 2) = 18

Reorder the terms:
(5 + t)(t + 2) = 18

Reorder the terms:
(5 + t)(2 + t) = 18

Multiply (5 + t) * (2 + t)
(5(2 + t) + t(2 + t)) = 18
((2 * 5 + t * 5) + t(2 + t)) = 18
((10 + 5t) + t(2 + t)) = 18
(10 + 5t + (2 * t + t * t)) = 18
(10 + 5t + (2t + t2)) = 18

Combine like terms: 5t + 2t = 7t
(10 + 7t + t2) = 18

Solving
10 + 7t + t2 = 18

Solving for variable 't'.

Reorder the terms:
10 + -18 + 7t + t2 = 18 + -18

Combine like terms: 10 + -18 = -8
-8 + 7t + t2 = 18 + -18

Combine like terms: 18 + -18 = 0
-8 + 7t + t2 = 0

Factor a trinomial.
(-8 + -1t)(1 + -1t) = 0

Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
Solution
t = {-8, 1}