100t^2-100t+25=0

Solution for 100t^2-100t+25=0 equation:

Simplifying
100t2 + -100t + 25 = 0

Reorder the terms:
25 + -100t + 100t2 = 0

Solving
25 + -100t + 100t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '25'.
25(1 + -4t + 4t2) = 0

Factor a trinomial.
25((1 + -2t)(1 + -2t)) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {0.5, 0.5}