(t+2)(t+4)=15

Solution for (t+2)(t+4)=15 equation:

Simplifying
(t + 2)(t + 4) = 15

Reorder the terms:
(2 + t)(t + 4) = 15

Reorder the terms:
(2 + t)(4 + t) = 15

Multiply (2 + t) * (4 + t)
(2(4 + t) + t(4 + t)) = 15
((4 * 2 + t * 2) + t(4 + t)) = 15
((8 + 2t) + t(4 + t)) = 15
(8 + 2t + (4 * t + t * t)) = 15
(8 + 2t + (4t + t2)) = 15

Combine like terms: 2t + 4t = 6t
(8 + 6t + t2) = 15

Solving
8 + 6t + t2 = 15

Solving for variable 't'.

Reorder the terms:
8 + -15 + 6t + t2 = 15 + -15

Combine like terms: 8 + -15 = -7
-7 + 6t + t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-7 + 6t + t2 = 0

Factor a trinomial.
(-7 + -1t)(1 + -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 '(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 = {-7, 1}