-5t^2+10t+3=3

Solution for -5t^2+10t+3=3 equation:

Simplifying
-5t2 + 10t + 3 = 3

Reorder the terms:
3 + 10t + -5t2 = 3

Add '-3' to each side of the equation.
3 + 10t + -3 + -5t2 = 3 + -3

Reorder the terms:
3 + -3 + 10t + -5t2 = 3 + -3

Combine like terms: 3 + -3 = 0
0 + 10t + -5t2 = 3 + -3
10t + -5t2 = 3 + -3

Combine like terms: 3 + -3 = 0
10t + -5t2 = 0

Solving
10t + -5t2 = 0

Solving for variable 't'.

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

Ignore the factor 5.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
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
Solution
t = {0, 2}