(t-vy)(2t+4vy)=0

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Solution for (t-vy)(2t+4vy)=0 equation:


Simplifying
(t + -1vy)(2t + 4vy) = 0

Multiply (t + -1vy) * (2t + 4vy)
(t(2t + 4vy) + -1vy * (2t + 4vy)) = 0
((2t * t + 4vy * t) + -1vy * (2t + 4vy)) = 0

Reorder the terms:
((4tvy + 2t2) + -1vy * (2t + 4vy)) = 0
((4tvy + 2t2) + -1vy * (2t + 4vy)) = 0
(4tvy + 2t2 + (2t * -1vy + 4vy * -1vy)) = 0
(4tvy + 2t2 + (-2tvy + -4v2y2)) = 0

Reorder the terms:
(4tvy + -2tvy + 2t2 + -4v2y2) = 0

Combine like terms: 4tvy + -2tvy = 2tvy
(2tvy + 2t2 + -4v2y2) = 0

Solving
2tvy + 2t2 + -4v2y2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(tvy + t2 + -2v2y2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(t + -1vy)' equal to zero and attempt to solve: Simplifying t + -1vy = 0 Solving t + -1vy = 0 Move all terms containing t to the left, all other terms to the right. Add 'vy' to each side of the equation. t + -1vy + vy = 0 + vy Combine like terms: -1vy + vy = 0 t + 0 = 0 + vy t = 0 + vy Remove the zero: t = vy Simplifying t = vy

Subproblem 2

Set the factor '(t + 2vy)' equal to zero and attempt to solve: Simplifying t + 2vy = 0 Solving t + 2vy = 0 Move all terms containing t to the left, all other terms to the right. Add '-2vy' to each side of the equation. t + 2vy + -2vy = 0 + -2vy Combine like terms: 2vy + -2vy = 0 t + 0 = 0 + -2vy t = 0 + -2vy Remove the zero: t = -2vy Simplifying t = -2vy

Solution

t = {vy, -2vy}

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