Solve (36-2x) * (24-2x) * x

Question

Simplify the expression

864 x - 120 x^{2} + 4 x^{3}

Evaluate

(36 - 2 x) (24 - 2 x) x

Multiply the terms

More Steps

Evaluate

(36 - 2 x) (24 - 2 x)

Apply the distributive property

36 \times 24 - 36 \times 2 x - 2 x \times 24 - (- 2 x \times 2 x)

Multiply the numbers

864 - 36 \times 2 x - 2 x \times 24 - (- 2 x \times 2 x)

Multiply the numbers

864 - 72 x - 2 x \times 24 - (- 2 x \times 2 x)

Multiply the numbers

864 - 72 x - 48 x - (- 2 x \times 2 x)

Multiply the terms

More Steps

Evaluate

- 2 x \times 2 x

Multiply the numbers

- 4 x \times x

Multiply the terms

- 4 x^{2}

864 - 72 x - 48 x - (- 4 x^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

864 - 72 x - 48 x + 4 x^{2}

Subtract the terms

More Steps

Evaluate

- 72 x - 48 x

Collect like terms by calculating the sum or difference of their coefficients

(- 72 - 48) x

Subtract the numbers

- 120 x

864 - 120 x + 4 x^{2}

(864 - 120 x + 4 x^{2}) x

Apply the distributive property

864 x - 120 x \times x + 4 x^{2} \times x

Multiply the terms

864 x - 120 x^{2} + 4 x^{2} \times x

Solution

More Steps

Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

864 x - 120 x^{2} + 4 x^{3}

Show Solution

Factor the expression

4 x (18 - x) (12 - x)

Evaluate

(36 - 2 x) (24 - 2 x) x

Factor the expression

2 (18 - x) (24 - 2 x) x

Factor the expression

2 (18 - x) \times 2 (12 - x) x

Solution

4 x (18 - x) (12 - x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 12, x_{3} = 18

Evaluate

(36 - 2 x) (24 - 2 x) x

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

(36 - 2 x) (24 - 2 x) x = 0

Separate the equation into 3 possible cases

36 - 2 x = 0 24 - 2 x = 0 x = 0

Solve the equation

More Steps

Evaluate

36 - 2 x = 0

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

- 2 x = 0 - 36

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

- 2 x = - 36

Change the signs on both sides of the equation

2 x = 36

Divide both sides

\frac{2 x}{2} = \frac{36}{2}

Divide the numbers

x = \frac{36}{2}

Divide the numbers

More Steps

Evaluate

\frac{36}{2}

Reduce the numbers

\frac{18}{1}

Calculate

18

x = 18

x = 18 24 - 2 x = 0 x = 0

Solve the equation

More Steps

Evaluate

24 - 2 x = 0

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

- 2 x = 0 - 24

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

- 2 x = - 24

Change the signs on both sides of the equation

2 x = 24

Divide both sides

\frac{2 x}{2} = \frac{24}{2}

Divide the numbers

x = \frac{24}{2}

Divide the numbers

More Steps

Evaluate

\frac{24}{2}

Reduce the numbers

\frac{12}{1}

Calculate

12

x = 12

x = 18 x = 12 x = 0

Solution

x_{1} = 0, x_{2} = 12, x_{3} = 18

Show Solution