What are the solutions to the equation (3x)(32x+1)(3x+5)=243 ?

The solutions to the equation (3x)(32x+1)(3x+5)=243 are x\approx 0.59532…

Find the zeros of (3x)(32x+1)(3x+5)=243

The zeros of (3x)(32x+1)(3x+5)=243 are x\approx 0.59532…

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(3 x) (32 x + 1) (3 x + 5) = 243

x \approx 0.59532 \dots

Solution steps

(3 x) (32 x + 1) (3 x + 5) = 243

Expand

(3 x) (32 x + 1) (3 x + 5) : 288 x^{3} + 489 x^{2} + 15 x

288 x^{3} + 489 x^{2} + 15 x = 243

Move

243

to the left side

288 x^{3} + 489 x^{2} + 15 x - 243 = 0

Find one solution for

288 x^{3} + 489 x^{2} + 15 x - 243 = 0

using Newton-Raphson:

x \approx 0.59532 \dots

Apply long division:

\frac{288 x ^{3} + 489 x ^{2} + 15 x - 243}{x - 0.59532 \dots} = 288 x^{2} + 660.45281 \dots x + 408.18227 \dots

288 x^{2} + 660.45281 \dots x + 408.18227 \dots \approx 0

Find one solution for

288 x^{2} + 660.45281 \dots x + 408.18227 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.59532 \dots

5 x^{3} = 9 x^{2}

- x^{3} - 12 x^{2} + 60 x - 64 = 0

2 x^{3} + 4 - 6 x = 0

- 12 + 14 (x^{2} - 3) = 2 (x^{2} - 3)^{2}

x^{3} + 6 x^{2} + 9 = 0

What are the solutions to the equation (3x)(32x+1)(3x+5)=243 ?
The solutions to the equation (3x)(32x+1)(3x+5)=243 are x\approx 0.59532…
Find the zeros of (3x)(32x+1)(3x+5)=243
The zeros of (3x)(32x+1)(3x+5)=243 are x\approx 0.59532…