What are the solutions to the equation 4x=x^3+3x^2 ?

The solutions to the equation 4x=x^3+3x^2 are x=0,x=1,x=-4

Find the zeros of 4x=x^3+3x^2

The zeros of 4x=x^3+3x^2 are x=0,x=1,x=-4

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4 x = x^{3} + 3 x^{2}

x = 0, x = 1, x = - 4

Solution steps

4 x = x^{3} + 3 x^{2}

Switch sides

x^{3} + 3 x^{2} = 4 x

Move

4 x

to the left side

x^{3} + 3 x^{2} - 4 x = 0

Factor

x^{3} + 3 x^{2} - 4 x : x (x - 1) (x + 4)

x (x - 1) (x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x + 4 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 4 = 0 : x = - 4

The solutions are

x = 0, x = 1, x = - 4

x (x + 3) (x - 1) = 0

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

x^{3} + 2 x^{2} - 5 x + 1 = 0

x^{3} - 5 x^{2} + 8 x - 6 = 0

6 = \frac{8 x ^{5}}{5} + b

What are the solutions to the equation 4x=x^3+3x^2 ?
The solutions to the equation 4x=x^3+3x^2 are x=0,x=1,x=-4
Find the zeros of 4x=x^3+3x^2
The zeros of 4x=x^3+3x^2 are x=0,x=1,x=-4