(y+nv)(4y+4nv)=

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Solution for (y+nv)(4y+4nv)= equation:


Simplifying
(y + nv)(4y + 4nv) = 0

Reorder the terms:
(nv + y)(4y + 4nv) = 0

Reorder the terms:
(nv + y)(4nv + 4y) = 0

Multiply (nv + y) * (4nv + 4y)
(nv(4nv + 4y) + y(4nv + 4y)) = 0
((4nv * nv + 4y * nv) + y(4nv + 4y)) = 0

Reorder the terms:
((4nvy + 4n2v2) + y(4nv + 4y)) = 0
((4nvy + 4n2v2) + y(4nv + 4y)) = 0
(4nvy + 4n2v2 + (4nv * y + 4y * y)) = 0
(4nvy + 4n2v2 + (4nvy + 4y2)) = 0

Reorder the terms:
(4nvy + 4nvy + 4n2v2 + 4y2) = 0

Combine like terms: 4nvy + 4nvy = 8nvy
(8nvy + 4n2v2 + 4y2) = 0

Solving
8nvy + 4n2v2 + 4y2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2nvy + n2v2 + y2) = 0

Factor a trinomial.
4((nv + y)(nv + y)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(nv + y)' equal to zero and attempt to solve: Simplifying nv + y = 0 Solving nv + y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1y' to each side of the equation. nv + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 nv + 0 = 0 + -1y nv = 0 + -1y Remove the zero: nv = -1y Divide each side by 'v'. n = -1v-1y Simplifying n = -1v-1y

Subproblem 2

Set the factor '(nv + y)' equal to zero and attempt to solve: Simplifying nv + y = 0 Solving nv + y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1y' to each side of the equation. nv + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 nv + 0 = 0 + -1y nv = 0 + -1y Remove the zero: nv = -1y Divide each side by 'v'. n = -1v-1y Simplifying n = -1v-1y

Solution

n = {-1v-1y, -1v-1y}

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