0=20t-5(t^2)+25

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Solution for 0=20t-5(t^2)+25 equation: 


Simplifying
0 = 20t + -5(t2) + 25

Reorder the terms:
0 = 25 + 20t + -5t2

Solving
0 = 25 + 20t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -25 = -25
-25 + -20t + 5t2 = 25 + 20t + -5t2 + -25 + -20t + 5t2

Reorder the terms:
-25 + -20t + 5t2 = 25 + -25 + 20t + -20t + -5t2 + 5t2

Combine like terms: 25 + -25 = 0
-25 + -20t + 5t2 = 0 + 20t + -20t + -5t2 + 5t2
-25 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2

Combine like terms: 20t + -20t = 0
-25 + -20t + 5t2 = 0 + -5t2 + 5t2
-25 + -20t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-25 + -20t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -4t + t2) = 0

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

Simplifying
5 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-1, 5}

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