Simply this Equation Step by Step

Solve:     (3x + 2)⁴  =  232

 

First:  find the fourth root of both sides:     3x + 2  =  232^1/4                            3x + 2  =  3.90276 ...

 

Second:  subtract 2 from both sides:               3x  =  232^1/4 - 2                      3x  =  1.90276 ...

 

Third:  divide both sides by 3:                            x  =  (232^1/4 - 2) / 3                x  =  0.63425,,,

Expand the following:
(3 x+2)^4 = 232

 

(3 x+2)^4 = sum_(k=0)^4 binomial(4, k) 2^(4-k) (3 x)^k = binomial(4, 0) (2)^4+binomial(4, 1) (2)^3 (3 x)+binomial(4, 2) (2)^2 (3 x)^2+binomial(4, 3) (2) (3 x)^3+binomial(4, 4) (3 x)^4 = 81 x^4+216 x^3+216 x^2+96 x+16:
81 x^4+216 x^3+216 x^2+96 x+16 = 232

 

Subtract 232 from both sides of 81 x^4+216 x^3+216 x^2+96 x+16 = 232:
81 x^4+216 x^3+216 x^2+96 x-232+16 = 232-232

 

232-232 = 0:
81 x^4+216 x^3+216 x^2+96 x-232+16 = 0

 

Grouping like terms, 81 x^4+216 x^3+216 x^2+96 x-232+16 = 81 x^4+216 x^3+216 x^2+96 x+(16-232):
81 x^4+216 x^3+216 x^2+96 x+(16-232) = 0

 

16-232 = -216:
Answer: |81 x^4+216 x^3+216 x^2+96 x+-216 = 0