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

The solutions to the equation 4x^2+4=3x^3+3x are x= 4/3 ,x=i,x=-i

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

The zeros of 4x^2+4=3x^3+3x are x= 4/3 ,x=i,x=-i

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

x = \frac{4}{3}, x = i, x = - i

Solution steps

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

Switch sides

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

Move

4

to the left side

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

Move

4 x^{2}

to the left side

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

Write in the standard form

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

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

Factor

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

(3 x - 4) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x - 4 = 0 or x^{2} + 1 = 0

Solve

3 x - 4 = 0 : x = \frac{4}{3}

Solve

x^{2} + 1 = 0 : x = i, x = - i

The solutions are

x = \frac{4}{3}, x = i, x = - i

2 (x + 1) - 6 x = 15 x^{21}

x, t = 64 - 6 x^{3}

4 a^{4} + 56 a^{3} + 196 a^{2} = 0

3 x^{3} - 24 x + 36 = 0

- x^{3} + 4 x^{2} - 9 x - 6 = 0

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