What are the solutions to the equation 4x^2-9=(2x^3)(2x-3) ?

The solutions to the equation 4x^2-9=(2x^3)(2x-3) are x= 3/2 ,x\approx 1.43112…

Find the zeros of 4x^2-9=(2x^3)(2x-3)

The zeros of 4x^2-9=(2x^3)(2x-3) are x= 3/2 ,x\approx 1.43112…

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4 x^{2} - 9 = (2 x^{3}) (2 x - 3)

x = \frac{3}{2}, x \approx 1.43112 \dots

Decimal Notation

x = 1.5, x = 1.43112 \dots

Solution steps

4 x^{2} - 9 = (2 x^{3}) (2 x - 3)

Expand

(2 x^{3}) (2 x - 3) : 4 x^{4} - 6 x^{3}

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

Switch sides

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

Move

9

to the left side

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

Move

4 x^{2}

to the left side

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

Write in the standard form

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

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

Factor

4 x^{4} - 6 x^{3} - 4 x^{2} + 9 : (2 x - 3) (2 x^{3} - 2 x - 3)

(2 x - 3) (2 x^{3} - 2 x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 3 = 0 or 2 x^{3} - 2 x - 3 = 0

Solve

2 x - 3 = 0 : x = \frac{3}{2}

Solve

2 x^{3} - 2 x - 3 = 0 : x \approx 1.43112 \dots

The solutions are

x = \frac{3}{2}, x \approx 1.43112 \dots

2 x^{4} = 9 x^{2}

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

11 x^{3} + 123 x^{2} + 23 x + 11

y, 4 x^{3} - 4 y = 0

z^{6} - 2 z^{3} + 2 = 0

What are the solutions to the equation 4x^2-9=(2x^3)(2x-3) ?
The solutions to the equation 4x^2-9=(2x^3)(2x-3) are x= 3/2 ,x\approx 1.43112…
Find the zeros of 4x^2-9=(2x^3)(2x-3)
The zeros of 4x^2-9=(2x^3)(2x-3) are x= 3/2 ,x\approx 1.43112…