6(t)=-5t^2+10t+1

Solution for 6(t)=-5t^2+10t+1 equation:

Simplifying
6(t) = -5t2 + 10t + 1

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

Solving
6t = 1 + 10t + -5t2

Solving for variable 't'.

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

Combine like terms: 6t + -10t = -4t
-1 + -4t + 5t2 = 1 + 10t + -5t2 + -1 + -10t + 5t2

Reorder the terms:
-1 + -4t + 5t2 = 1 + -1 + 10t + -10t + -5t2 + 5t2

Combine like terms: 1 + -1 = 0
-1 + -4t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2
-1 + -4t + 5t2 = 10t + -10t + -5t2 + 5t2

Combine like terms: 10t + -10t = 0
-1 + -4t + 5t2 = 0 + -5t2 + 5t2
-1 + -4t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-1 + -4t + 5t2 = 0

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

Subproblem 1
Set the factor '(-1 + -5t)' equal to zero and attempt to solve:

Simplifying
-1 + -5t = 0

Solving
-1 + -5t = 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 + -5t = 0 + 1

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

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

Divide each side by '-5'.
t = -0.2

Simplifying
t = -0.2
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 = {-0.2, 1}