t^2+2t+1=25

Solution for t^2+2t+1=25 equation:

Simplifying
t2 + 2t + 1 = 25

Reorder the terms:
1 + 2t + t2 = 25

Solving
1 + 2t + t2 = 25

Solving for variable 't'.

Reorder the terms:
1 + -25 + 2t + t2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 2t + t2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 2t + t2 = 0

Factor a trinomial.
(-6 + -1t)(4 + -1t) = 0

Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-6, 4}