Question

What is the solution of equation for -3x^3 -x^2 + 54x -40 = 2x^2 + 6X + 20

Answer 1

The solved given equation is
`x^3+x^2+16x-20=(x-2)(x-2)(x+5)`.

Explanation:

Given equation is
`-3x^3-x^2+54x-40=2x^2+6x+20`

To solve the given equation:

`-3x^3-x^2+54x-40-2x^2-6x-20=0`

`-3x^3-3x^2+48x-60=0`

Multiply the above equation into
`-(1)/(3)` on both sides

`-3x^3-3x^2+48x-60* (-(1)/(3))=0* (-(1)/(3))`

`x^3+x^2+16x-20=0`

To sove the equation by using synthetic division method

2_| 1 1 -16 20

0 2 6 -20

___________

1 3 -10 0

Therefore x-2 is a factor

Therefore the quadratic equation is
`x^2+3x-10=0`

(x-2)(x+5)=0

(x-2)=0 or (x+5)=0

`x^2+3x-10=(x-2)(x+5)`

Therefore the factors are x-2,x-2,x+5

Therefore the solved given equation is
`x^3+x^2+16x-20=(x-2)(x-2)(x+5)`