What are the solutions to the equation (6x+10)(7x-2)(8x+4)=180 ?

The solutions to the equation (6x+10)(7x-2)(8x+4)=180 are x\approx 0.52439…

Find the zeros of (6x+10)(7x-2)(8x+4)=180

The zeros of (6x+10)(7x-2)(8x+4)=180 are x\approx 0.52439…

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(6 x + 10) (7 x - 2) (8 x + 4) = 180

x \approx 0.52439 \dots

Solution steps

(6 x + 10) (7 x - 2) (8 x + 4) = 180

Expand

(6 x + 10) (7 x - 2) (8 x + 4) : 336 x^{3} + 632 x^{2} + 72 x - 80

336 x^{3} + 632 x^{2} + 72 x - 80 = 180

Move

180

to the left side

336 x^{3} + 632 x^{2} + 72 x - 260 = 0

Find one solution for

336 x^{3} + 632 x^{2} + 72 x - 260 = 0

using Newton-Raphson:

x \approx 0.52439 \dots

Apply long division:

\frac{336 x ^{3} + 632 x ^{2} + 72 x - 260}{x - 0.52439 \dots} = 336 x^{2} + 808.19587 \dots x + 495.81183 \dots

336 x^{2} + 808.19587 \dots x + 495.81183 \dots \approx 0

Find one solution for

336 x^{2} + 808.19587 \dots x + 495.81183 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.52439 \dots

3 x^{4} + 3 x^{3} - 17 x^{2} + x - 6 = 0

t^{3} = 512

x^{3} - 5 x^{2} + 5 x + 7 = 7

x^{8} + 8 x + 16 = 0

9 + 3 a^{3} = 12

What are the solutions to the equation (6x+10)(7x-2)(8x+4)=180 ?
The solutions to the equation (6x+10)(7x-2)(8x+4)=180 are x\approx 0.52439…
Find the zeros of (6x+10)(7x-2)(8x+4)=180
The zeros of (6x+10)(7x-2)(8x+4)=180 are x\approx 0.52439…