110+t^2=190+2t

Solution for 110+t^2=190+2t equation:

Simplifying
110 + t2 = 190 + 2t

Solving
110 + t2 = 190 + 2t

Solving for variable 't'.

Reorder the terms:
110 + -190 + -2t + t2 = 190 + 2t + -190 + -2t

Combine like terms: 110 + -190 = -80
-80 + -2t + t2 = 190 + 2t + -190 + -2t

Reorder the terms:
-80 + -2t + t2 = 190 + -190 + 2t + -2t

Combine like terms: 190 + -190 = 0
-80 + -2t + t2 = 0 + 2t + -2t
-80 + -2t + t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-80 + -2t + t2 = 0

Factor a trinomial.
(-8 + -1t)(10 + -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 '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Solution
t = {-8, 10}