(t+2)(t+2)-12(t+2)+35=0

Solution for (t+2)(t+2)-12(t+2)+35=0 equation:

Simplifying
(t + 2)(t + 2) + -12(t + 2) + 35 = 0

Reorder the terms:
(2 + t)(t + 2) + -12(t + 2) + 35 = 0

Reorder the terms:
(2 + t)(2 + t) + -12(t + 2) + 35 = 0

Multiply (2 + t) * (2 + t)
(2(2 + t) + t(2 + t)) + -12(t + 2) + 35 = 0
((2 * 2 + t * 2) + t(2 + t)) + -12(t + 2) + 35 = 0
((4 + 2t) + t(2 + t)) + -12(t + 2) + 35 = 0
(4 + 2t + (2 * t + t * t)) + -12(t + 2) + 35 = 0
(4 + 2t + (2t + t2)) + -12(t + 2) + 35 = 0

Combine like terms: 2t + 2t = 4t
(4 + 4t + t2) + -12(t + 2) + 35 = 0

Reorder the terms:
4 + 4t + t2 + -12(2 + t) + 35 = 0
4 + 4t + t2 + (2 * -12 + t * -12) + 35 = 0
4 + 4t + t2 + (-24 + -12t) + 35 = 0

Reorder the terms:
4 + -24 + 35 + 4t + -12t + t2 = 0

Combine like terms: 4 + -24 = -20
-20 + 35 + 4t + -12t + t2 = 0

Combine like terms: -20 + 35 = 15
15 + 4t + -12t + t2 = 0

Combine like terms: 4t + -12t = -8t
15 + -8t + t2 = 0

Solving
15 + -8t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -1t)(5 + -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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {3, 5}