What are the solutions to the equation pi(4/3+2n+n^2)=(4pi)/3+npi ?

The solutions to the equation pi(4/3+2n+n^2)=(4pi)/3+npi are n=0,n=-1

Find the zeros of pi(4/3+2n+n^2)=(4pi)/3+npi

The zeros of pi(4/3+2n+n^2)=(4pi)/3+npi are n=0,n=-1

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π (\frac{4}{3} + 2 n + n^{2}) = \frac{4 π}{3} + nπ

n = 0, n = - 1

Solution steps

π (\frac{4}{3} + 2 n + n^{2}) = \frac{4 π}{3} + nπ

Multiply both sides by

3

3 π (\frac{4}{3} + 2 n + n^{2}) = 4 π + 3 πn

Expand

3 π (\frac{4}{3} + 2 n + n^{2}) : 4 π + 6 πn + 3 π n^{2}

4 π + 6 πn + 3 π n^{2} = 4 π + 3 πn

Move

3 πn

to the left side

4 π + 3 π n^{2} + 3 πn = 4 π

Move

4 π

to the left side

3 π n^{2} + 3 πn = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 3 π \pm ( 3 π ) ^{2} - 4 \cdot 3 π 0}{2 \cdot 3 π}

(3 π)^{2} - 4 \cdot 3 π 0 = 3 π

n_{1, 2} = \frac{- 3 π \pm 3 π}{2 \cdot 3 π}

Separate the solutions

n_{1} = \frac{- 3 π + 3 π}{2 \cdot 3 π}, n_{2} = \frac{- 3 π - 3 π}{2 \cdot 3 π}

n = \frac{- 3 π + 3 π}{2 \cdot 3 π} : 0

n = \frac{- 3 π - 3 π}{2 \cdot 3 π} : - 1

The solutions to the quadratic equation are:

n = 0, n = - 1

3 x (x + 7) = 0

5 x^{2} + 7 x - 50 = 4 x^{2} + 6 x + 22

- 2 x^{2} - 4 = 0

(x + 2) x = 24

x, x^{2} + 8 x + 4 = 0

What are the solutions to the equation pi(4/3+2n+n^2)=(4pi)/3+npi ?
The solutions to the equation pi(4/3+2n+n^2)=(4pi)/3+npi are n=0,n=-1
Find the zeros of pi(4/3+2n+n^2)=(4pi)/3+npi
The zeros of pi(4/3+2n+n^2)=(4pi)/3+npi are n=0,n=-1