Solve 4x^6=3x^3(2x^5)

Question

Solve the equation

x_{1} = - \frac{6}{3}, x_{2} = 0, x_{3} = \frac{6}{3}

Alternative Form

x_{1} \approx - 0.816497, x_{2} = 0, x_{3} \approx 0.816497

Evaluate

4 x^{6} = 3 x^{3} \times 2 x^{5}

Multiply

More Steps

Evaluate

3 x^{3} \times 2 x^{5}

Multiply the terms

6 x^{3} \times x^{5}

Multiply the terms with the same base by adding their exponents

6 x^{3 + 5}

Add the numbers

6 x^{8}

4 x^{6} = 6 x^{8}

Add or subtract both sides

4 x^{6} - 6 x^{8} = 0

Factor the expression

2 x^{6} (2 - 3 x^{2}) = 0

Divide both sides

x^{6} (2 - 3 x^{2}) = 0

Separate the equation into 2 possible cases

x^{6} = 0 2 - 3 x^{2} = 0

The only way a power can be 0 is when the base equals 0

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

Solve the equation

More Steps

Evaluate

2 - 3 x^{2} = 0

Move the constant to the right-hand side and change its sign

- 3 x^{2} = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 3 x^{2} = - 2

Change the signs on both sides of the equation

3 x^{2} = 2

Divide both sides

\frac{3 x ^{2}}{3} = \frac{2}{3}

Divide the numbers

x^{2} = \frac{2}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{2}{3}

Simplify the expression

More Steps

Evaluate

\frac{2}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{2}{3}

Multiply by the Conjugate

\frac{2 \times 3}{3 \times 3}

Multiply the numbers

\frac{6}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6}{3}

x = \pm \frac{6}{3}

Separate the equation into 2 possible cases

x = \frac{6}{3} x = - \frac{6}{3}

x = 0 x = \frac{6}{3} x = - \frac{6}{3}

Solution

x_{1} = - \frac{6}{3}, x_{2} = 0, x_{3} = \frac{6}{3}

Alternative Form

x_{1} \approx - 0.816497, x_{2} = 0, x_{3} \approx 0.816497

Show Solution