Solve (50-2x)(30-2x)(x)

Question

Simplify the expression

1500 x - 160 x^{2} + 4 x^{3}

Evaluate

(50 - 2 x) (30 - 2 x) x

Multiply the terms

More Steps

Evaluate

(50 - 2 x) (30 - 2 x)

Apply the distributive property

50 \times 30 - 50 \times 2 x - 2 x \times 30 - (- 2 x \times 2 x)

Multiply the numbers

1500 - 50 \times 2 x - 2 x \times 30 - (- 2 x \times 2 x)

Multiply the numbers

1500 - 100 x - 2 x \times 30 - (- 2 x \times 2 x)

Multiply the numbers

1500 - 100 x - 60 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}

1500 - 100 x - 60 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

1500 - 100 x - 60 x + 4 x^{2}

Subtract the terms

More Steps

Evaluate

- 100 x - 60 x

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

(- 100 - 60) x

Subtract the numbers

- 160 x

1500 - 160 x + 4 x^{2}

(1500 - 160 x + 4 x^{2}) x

Apply the distributive property

1500 x - 160 x \times x + 4 x^{2} \times x

Multiply the terms

1500 x - 160 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}

1500 x - 160 x^{2} + 4 x^{3}

Show Solution

Factor the expression

4 x (25 - x) (15 - x)

Evaluate

(50 - 2 x) (30 - 2 x) x

Factor the expression

2 (25 - x) (30 - 2 x) x

Factor the expression

2 (25 - x) \times 2 (15 - x) x

Solution

4 x (25 - x) (15 - x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 15, x_{3} = 25

Evaluate

(50 - 2 x) (30 - 2 x) x

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

(50 - 2 x) (30 - 2 x) x = 0

Separate the equation into 3 possible cases

50 - 2 x = 0 30 - 2 x = 0 x = 0

Solve the equation

More Steps

Evaluate

50 - 2 x = 0

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

- 2 x = 0 - 50

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

- 2 x = - 50

Change the signs on both sides of the equation

2 x = 50

Divide both sides

\frac{2 x}{2} = \frac{50}{2}

Divide the numbers

x = \frac{50}{2}

Divide the numbers

More Steps

Evaluate

\frac{50}{2}

Reduce the numbers

\frac{25}{1}

Calculate

25

x = 25

x = 25 30 - 2 x = 0 x = 0

Solve the equation

More Steps

Evaluate

30 - 2 x = 0

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

- 2 x = 0 - 30

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

- 2 x = - 30

Change the signs on both sides of the equation

2 x = 30

Divide both sides

\frac{2 x}{2} = \frac{30}{2}

Divide the numbers

x = \frac{30}{2}

Divide the numbers

More Steps

Evaluate

\frac{30}{2}

Reduce the numbers

\frac{15}{1}

Calculate

15

x = 15

x = 25 x = 15 x = 0

Solution

x_{1} = 0, x_{2} = 15, x_{3} = 25

Show Solution