Solve 6x^(3) 8x^(2)-4x

Question

Simplify the expression

48 x^{5} - 4 x

Evaluate

6 x^{3} \times 8 x^{2} - 4 x

Solution

More Steps

Evaluate

6 x^{3} \times 8 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

48 x^{3 + 2}

Add the numbers

48 x^{5}

48 x^{5} - 4 x

Show Solution

Factor the expression

4 x (12 x^{4} - 1)

Evaluate

6 x^{3} \times 8 x^{2} - 4 x

Multiply

More Steps

Evaluate

6 x^{3} \times 8 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

48 x^{3 + 2}

Add the numbers

48 x^{5}

48 x^{5} - 4 x

Rewrite the expression

4 x \times 12 x^{4} - 4 x

Solution

4 x (12 x^{4} - 1)

Show Solution

Find the roots

x_{1} = - \frac{4 108}{6}, x_{2} = 0, x_{3} = \frac{4 108}{6}

Alternative Form

x_{1} \approx - 0.537285, x_{2} = 0, x_{3} \approx 0.537285

Evaluate

6 x^{3} \times 8 x^{2} - 4 x

To find the roots of the expression,set the expression equal to 0

6 x^{3} \times 8 x^{2} - 4 x = 0

Multiply

More Steps

Multiply the terms

6 x^{3} \times 8 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

48 x^{3 + 2}

Add the numbers

48 x^{5}

48 x^{5} - 4 x = 0

Factor the expression

4 x (12 x^{4} - 1) = 0

Divide both sides

x (12 x^{4} - 1) = 0

Separate the equation into 2 possible cases

x = 0 12 x^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

12 x^{4} - 1 = 0

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

12 x^{4} = 0 + 1

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

12 x^{4} = 1

Divide both sides

\frac{12 x ^{4}}{12} = \frac{1}{12}

Divide the numbers

x^{4} = \frac{1}{12}

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

x = \pm 4 \frac{1}{12}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{12}

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

\frac{4 1}{4 12}

Simplify the radical expression

\frac{1}{4 12}

Multiply by the Conjugate

\frac{4 1 2 ^{3}}{4 12 \times 4 1 2 ^{3}}

Simplify

\frac{2 4 108}{4 12 \times 4 1 2 ^{3}}

Multiply the numbers

\frac{2 4 108}{12}

Cancel out the common factor 2

\frac{4 108}{6}

x = \pm \frac{4 108}{6}

Separate the equation into 2 possible cases

x = \frac{4 108}{6} x = - \frac{4 108}{6}

x = 0 x = \frac{4 108}{6} x = - \frac{4 108}{6}

Solution

x_{1} = - \frac{4 108}{6}, x_{2} = 0, x_{3} = \frac{4 108}{6}

Alternative Form

x_{1} \approx - 0.537285, x_{2} = 0, x_{3} \approx 0.537285

Show Solution