What is the value of x

4x^3+3=867

Minus 867 from both sides

4x³-864=0

undistribute 4

4 (x³-216) = 0

factor differnce of 2 perfect cubes

remember that a³-b³ = (a-b) (a²+ab+b²)

so

(4) (x³-6³) = (4) (x-6) (x²+6x+36) = 0

set each to 0

x-6=0

x=6

x²-6x+36=0

no real numbers will work for x

x=6

Isolate the x:

4x^3 = 864,

x^3 = 216

x = 6