t^2-6t=20+2t

Solution for t^2-6t=20+2t equation:

Simplifying
t2 + -6t = 20 + 2t

Reorder the terms:
-6t + t2 = 20 + 2t

Solving
-6t + t2 = 20 + 2t

Solving for variable 't'.

Reorder the terms:
-20 + -6t + -2t + t2 = 20 + 2t + -20 + -2t

Combine like terms: -6t + -2t = -8t
-20 + -8t + t2 = 20 + 2t + -20 + -2t

Reorder the terms:
-20 + -8t + t2 = 20 + -20 + 2t + -2t

Combine like terms: 20 + -20 = 0
-20 + -8t + t2 = 0 + 2t + -2t
-20 + -8t + t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-20 + -8t + t2 = 0

Factor a trinomial.
(-2 + -1t)(10 + -1t) = 0

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
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 = {-2, 10}