how can i solve this r(x)=8x^3+12x^2-2x-3?

r (x) = 8x^3 + 12x^2 - 2x - 3

r (x) = 8 (x - 1/2) (x + 1/2) (x + 3/2)

r (x) = [ 2 (x - 1/2) ] [ 2 (x + 1/2) ] [ 2 (x + 3/2) ]

r (x) = (2x - 1) (2x + 1) (2x + 3)


If you want to solve r (x) = 0 then x = - 1/2 x = 1/2 and x = - 3/2

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a^2 - b^2 ≡ (a + b)(a - b)

Factor completely.
r(x) = 8x^3 + 12x^2 - 2x - 3
r(x) = (8x^3 + 12x^2) - (2x + 3)
r(x) = 4x^2(2x + 3) - 1(2x + 3)
r(x) = (2x + 3)(4x^2 - 1)
r(x) = (2x + 3)[(2x)^2 - 1^2]
r(x) = (2x + 3)(2x + 1)(2x - 1)

What is there to solve? you have given only a function. You must have an equation to solve. Revise the wording of the problem. Will you?

What do you mean by "SOLVE" ?