H(t)=t^2-2t

Solution for H(t)=t^2-2t equation:

Simplifying
H(t) = t2 + -2t

Multiply H * t
tH = t2 + -2t

Reorder the terms:
tH = -2t + t2

Solving
tH = -2t + t2

Solving for variable 't'.

Reorder the terms:
2t + tH + -1t2 = -2t + t2 + 2t + -1t2

Reorder the terms:
2t + tH + -1t2 = -2t + 2t + t2 + -1t2

Combine like terms: -2t + 2t = 0
2t + tH + -1t2 = 0 + t2 + -1t2
2t + tH + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
2t + tH + -1t2 = 0

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

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 + H + -1t)' equal to zero and attempt to solve:

Simplifying
2 + H + -1t = 0

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

Reorder the terms:
2 + -2 + H + -1t = 0 + -2

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

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

Add '-1H' to each side of the equation.
H + -1H + -1t = -2 + -1H

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

Divide each side by '-1'.
t = 2 + H

Simplifying
t = 2 + H
Solution
t = {0, 2 + H}