Solve 2x^3 6x^2-36x

Question

Simplify the expression

12 x^{5} - 36 x

Evaluate

2 x^{3} \times 6 x^{2} - 36 x

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{3 + 2}

Add the numbers

12 x^{5}

12 x^{5} - 36 x

Show Solution

12 x (x^{4} - 3)

Evaluate

2 x^{3} \times 6 x^{2} - 36 x

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{3 + 2}

Add the numbers

12 x^{5}

12 x^{5} - 36 x

Rewrite the expression

12 x \times x^{4} - 12 x \times 3

Solution

12 x (x^{4} - 3)

Show Solution

x_{1} = - 43, x_{2} = 0, x_{3} = 43

Alternative Form

x_{1} \approx - 1.316074, x_{2} = 0, x_{3} \approx 1.316074

Evaluate

2 x^{3} \times 6 x^{2} - 36 x

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

2 x^{3} \times 6 x^{2} - 36 x = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{3 + 2}

Add the numbers

12 x^{5}

12 x^{5} - 36 x = 0

Factor the expression

12 x (x^{4} - 3) = 0

Divide both sides

x (x^{4} - 3) = 0

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

x^{4} - 3 = 0

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

x^{4} = 0 + 3

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

x^{4} = 3

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

x = \pm 43

Separate the equation into 2 possible cases

x = 43 x = - 43

x = 0 x = 43 x = - 43

Solution

x_{1} = - 43, x_{2} = 0, x_{3} = 43

Alternative Form

x_{1} \approx - 1.316074, x_{2} = 0, x_{3} \approx 1.316074

Show Solution