What are the solutions to the equation 5z^2-45=8z^3-72z ?

The solutions to the equation 5z^2-45=8z^3-72z are z= 5/8 ,z=-3,z=3

Find the zeros of 5z^2-45=8z^3-72z

The zeros of 5z^2-45=8z^3-72z are z= 5/8 ,z=-3,z=3

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5 z^{2} - 45 = 8 z^{3} - 72 z

z = \frac{5}{8}, z = - 3, z = 3

Decimal Notation

z = 0.625, z = - 3, z = 3

Solution steps

5 z^{2} - 45 = 8 z^{3} - 72 z

Switch sides

8 z^{3} - 72 z = 5 z^{2} - 45

Move

45

to the left side

8 z^{3} - 72 z + 45 = 5 z^{2}

Move

5 z^{2}

to the left side

8 z^{3} - 72 z + 45 - 5 z^{2} = 0

Write in the standard form

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

8 z^{3} - 5 z^{2} - 72 z + 45 = 0

Factor

8 z^{3} - 5 z^{2} - 72 z + 45 : (8 z - 5) (z + 3) (z - 3)

(8 z - 5) (z + 3) (z - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

8 z - 5 = 0 or z + 3 = 0 or z - 3 = 0

Solve

8 z - 5 = 0 : z = \frac{5}{8}

Solve

z + 3 = 0 : z = - 3

Solve

z - 3 = 0 : z = 3

The solutions are

z = \frac{5}{8}, z = - 3, z = 3

x^{3} - 9 x^{2} + 36 x - 36 = 0

x^{3} - 7 x^{2} + 36 = 0

3 x^{4} + 4 x^{3} - 6 x^{2} - 12 x = 0

16 z^{4} = 1

(\frac{a ^{2}}{3})^{2} + (a)^{2} = 50

What are the solutions to the equation 5z^2-45=8z^3-72z ?
The solutions to the equation 5z^2-45=8z^3-72z are z= 5/8 ,z=-3,z=3
Find the zeros of 5z^2-45=8z^3-72z
The zeros of 5z^2-45=8z^3-72z are z= 5/8 ,z=-3,z=3