What are the solutions to the equation (u+9)^3=-(u+9)^2 ?

The solutions to the equation (u+9)^3=-(u+9)^2 are u=-9,u=-10

Find the zeros of (u+9)^3=-(u+9)^2

The zeros of (u+9)^3=-(u+9)^2 are u=-9,u=-10

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(u + 9)^{3} = - (u + 9)^{2}

u = - 9, u = - 10

Solution steps

(u + 9)^{3} = - (u + 9)^{2}

Expand

(u + 9)^{3} : u^{3} + 27 u^{2} + 243 u + 729

Expand

- (u + 9)^{2} : - u^{2} - 18 u - 81

u^{3} + 27 u^{2} + 243 u + 729 = - u^{2} - 18 u - 81

Move

81

to the left side

u^{3} + 27 u^{2} + 243 u + 810 = - u^{2} - 18 u

Move

18 u

to the left side

u^{3} + 27 u^{2} + 261 u + 810 = - u^{2}

Move

u^{2}

to the left side

u^{3} + 28 u^{2} + 261 u + 810 = 0

Factor

u^{3} + 28 u^{2} + 261 u + 810 : (u + 9)^{2} (u + 10)

(u + 9)^{2} (u + 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

u + 9 = 0 or u + 10 = 0

Solve

u + 9 = 0 : u = - 9

Solve

u + 10 = 0 : u = - 10

The solutions are

u = - 9, u = - 10

2 x^{3} + x^{2} - 100 x - 25 = 0

y^{4} - 81 = 0

x^{3} - 3 x + \frac{9}{8} = 0

4 x - x^{2} - 3 = (x - 2) (x^{2} - 4 x + 3)

3 x^{4} - 10 x^{3} - 24 x^{2} - 6 x + 5 = 0

What are the solutions to the equation (u+9)^3=-(u+9)^2 ?
The solutions to the equation (u+9)^3=-(u+9)^2 are u=-9,u=-10
Find the zeros of (u+9)^3=-(u+9)^2
The zeros of (u+9)^3=-(u+9)^2 are u=-9,u=-10