Algebra 2 help easy 10 points ? Solve all polynomial equation

8x^5 + 10x^4 = 4x^3 + 5x^3

NOTE: I'm assuming that 5x^3 is supposed to be 5x^2, because that makes more sense...


Set the equation to 0 and factor

8x^5 + 10x^4 - 4x^3 - 5x^2 = 0

I'm going to factor by grouping.

8x^5 - 4x^3 + 10x^4 - 5x^2 = 0
4x^3(2x^2-1) + 5x^2(2x^2 - 1)=0
(2x^2-1)(4x^3+5x^2)=0
(2x^2-1)x^2(4x+5)

x^2=0
and
4x+5=0

x = -5/4, and 0 (with a multiplicity of 2)
So now you need to use the quadratic equation to find the 2 x values of (2x^2-1)

a=2
b=0
c=-1

x=(-0+/-√(0^2-4(2)(-1)))/2(2)
x= (+/-√8)/4
x = (+/-2√2)/4
x = (+/-√2)/2

So all your x values are:

x = √2/2
x = -√2/2
x = 0 (With a multiplicity of 2)
x = -4/5

well firstly add like term and put them all on one side:

8x^5 + 10x^4 - 9x^3 = 0

then you have to reduce it:

x^3(8x^2 + 10x - 9) = 0

Then I get lost but it's a start at leats :)