6=-5(t)(t)+10t+1

Solution for 6=-5(t)(t)+10t+1 equation:

Simplifying
6 = -5(t)(t) + 10t + 1

Multiply t * t
6 = -5t2 + 10t + 1

Reorder the terms:
6 = 1 + 10t + -5t2

Solving
6 = 1 + 10t + -5t2

Solving for variable 't'.

Combine like terms: 6 + -1 = 5
5 + -10t + 5t2 = 1 + 10t + -5t2 + -1 + -10t + 5t2

Reorder the terms:
5 + -10t + 5t2 = 1 + -1 + 10t + -10t + -5t2 + 5t2

Combine like terms: 1 + -1 = 0
5 + -10t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2
5 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2

Combine like terms: 10t + -10t = 0
5 + -10t + 5t2 = 0 + -5t2 + 5t2
5 + -10t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
5 + -10t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -2t + t2) = 0

Factor a trinomial.
5((1 + -1t)(1 + -1t)) = 0

Ignore the factor 5.
Subproblem 1
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
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 = {1, 1}