v^2+16=-2-6v^2-27v

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Solution for v^2+16=-2-6v^2-27v equation:


Simplifying
v2 + 16 = -2 + -6v2 + -27v

Reorder the terms:
16 + v2 = -2 + -6v2 + -27v

Reorder the terms:
16 + v2 = -2 + -27v + -6v2

Solving
16 + v2 = -2 + -27v + -6v2

Solving for variable 'v'.

Reorder the terms:
16 + 2 + 27v + v2 + 6v2 = -2 + -27v + -6v2 + 2 + 27v + 6v2

Combine like terms: 16 + 2 = 18
18 + 27v + v2 + 6v2 = -2 + -27v + -6v2 + 2 + 27v + 6v2

Combine like terms: v2 + 6v2 = 7v2
18 + 27v + 7v2 = -2 + -27v + -6v2 + 2 + 27v + 6v2

Reorder the terms:
18 + 27v + 7v2 = -2 + 2 + -27v + 27v + -6v2 + 6v2

Combine like terms: -2 + 2 = 0
18 + 27v + 7v2 = 0 + -27v + 27v + -6v2 + 6v2
18 + 27v + 7v2 = -27v + 27v + -6v2 + 6v2

Combine like terms: -27v + 27v = 0
18 + 27v + 7v2 = 0 + -6v2 + 6v2
18 + 27v + 7v2 = -6v2 + 6v2

Combine like terms: -6v2 + 6v2 = 0
18 + 27v + 7v2 = 0

Factor a trinomial.
(3 + v)(6 + 7v) = 0

Subproblem 1

Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3

Subproblem 2

Set the factor '(6 + 7v)' equal to zero and attempt to solve: Simplifying 6 + 7v = 0 Solving 6 + 7v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7v = 0 + -6 7v = 0 + -6 Combine like terms: 0 + -6 = -6 7v = -6 Divide each side by '7'. v = -0.8571428571 Simplifying v = -0.8571428571

Solution

v = {-3, -0.8571428571}

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