What are the solutions to the equation x^3+3x^2=25x+75 ?

The solutions to the equation x^3+3x^2=25x+75 are x=-3,x=-5,x=5

Find the zeros of x^3+3x^2=25x+75

The zeros of x^3+3x^2=25x+75 are x=-3,x=-5,x=5

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x^{3} + 3 x^{2} = 25 x + 75

x = - 3, x = - 5, x = 5

Solution steps

x^{3} + 3 x^{2} = 25 x + 75

Move

75

to the left side

x^{3} + 3 x^{2} - 75 = 25 x

Move

25 x

to the left side

x^{3} + 3 x^{2} - 75 - 25 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + 3 x^{2} - 25 x - 75 = 0

Factor

x^{3} + 3 x^{2} - 25 x - 75 : (x + 3) (x + 5) (x - 5)

(x + 3) (x + 5) (x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x + 5 = 0 or x - 5 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x + 5 = 0 : x = - 5

Solve

x - 5 = 0 : x = 5

The solutions are

x = - 3, x = - 5, x = 5

x^{3} = 5 x

z^{5} + 32 = 0

x^{3} + 6 x^{2} + 4 x + 24 = 0

x^{3} - 2 x^{2} - x + 7 = x^{2} - 3 x + 7

a^{3} - 3 a - 2 = 0

What are the solutions to the equation x^3+3x^2=25x+75 ?
The solutions to the equation x^3+3x^2=25x+75 are x=-3,x=-5,x=5
Find the zeros of x^3+3x^2=25x+75
The zeros of x^3+3x^2=25x+75 are x=-3,x=-5,x=5