0=23t-10t^2+5

Solution for 0=23t-10t^2+5 equation:

Simplifying
0 = 23t + -10t2 + 5

Reorder the terms:
0 = 5 + 23t + -10t2

Solving
0 = 5 + 23t + -10t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -23t + 10t2 = 5 + 23t + -10t2 + -5 + -23t + 10t2

Reorder the terms:
-5 + -23t + 10t2 = 5 + -5 + 23t + -23t + -10t2 + 10t2

Combine like terms: 5 + -5 = 0
-5 + -23t + 10t2 = 0 + 23t + -23t + -10t2 + 10t2
-5 + -23t + 10t2 = 23t + -23t + -10t2 + 10t2

Combine like terms: 23t + -23t = 0
-5 + -23t + 10t2 = 0 + -10t2 + 10t2
-5 + -23t + 10t2 = -10t2 + 10t2

Combine like terms: -10t2 + 10t2 = 0
-5 + -23t + 10t2 = 0

Factor a trinomial.
(-1 + -5t)(5 + -2t) = 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 '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {-0.2, 2.5}