Now we have a cubic equation, which can be solved using various methods such as factoring, synthetic division, or using a numerical method like Newton's method. The solutions to this equation will give us the values of x that satisfy the original equation.
To solve the equation (х-2)(х^2+8х+16)=7(4+Х), we first need to expand both sides of the equation:
(х-2)(х^2+8х+16) = 7(4+Х)
х^3 + 8х^2 + 16х - 2х^ + 16х - 32 = 28 + 7х
Next, simplify the equation by combining like terms:
х^3 + 8х^2 + 30х - 32 = 28 + 7х
х^3 + 8х^2 + 23х - 60 = 0
Now we have a cubic equation, which can be solved using various methods such as factoring, synthetic division, or using a numerical method like Newton's method. The solutions to this equation will give us the values of x that satisfy the original equation.