Solve (3x-4)(x-5) (x 1)(3x 15)

Question

Simplify the expression

Solution

135 x^{4} - 855 x^{3} + 900 x^{2}

Evaluate

(3 x - 4) (x - 5) (x \times 1) (3 x \times 15)

Remove the parentheses

(3 x - 4) (x - 5) x \times 1 \times 3 x \times 15

Rewrite the expression

(3 x - 4) (x - 5) x \times 3 x \times 15

Multiply the terms

(3 x - 4) (x - 5) x^{2} \times 3 \times 15

Multiply the terms

(3 x - 4) (x - 5) x^{2} \times 45

Use the commutative property to reorder the terms

(3 x - 4) (x - 5) \times 45 x^{2}

Use the commutative property to reorder the terms

45 (3 x - 4) (x - 5) x^{2}

Multiply the terms

More Steps

Evaluate

45 (3 x - 4)

Apply the distributive property

45 \times 3 x - 45 \times 4

Multiply the numbers

135 x - 45 \times 4

Multiply the numbers

135 x - 180

(135 x - 180) (x - 5) x^{2}

Multiply the terms

More Steps

Evaluate

(135 x - 180) (x - 5)

Apply the distributive property

135 x \times x - 135 x \times 5 - 180 x - (- 180 \times 5)

Multiply the terms

135 x^{2} - 135 x \times 5 - 180 x - (- 180 \times 5)

Multiply the numbers

135 x^{2} - 675 x - 180 x - (- 180 \times 5)

Multiply the numbers

135 x^{2} - 675 x - 180 x - (- 900)

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

135 x^{2} - 675 x - 180 x + 900

Subtract the terms

More Steps

Evaluate

- 675 x - 180 x

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

(- 675 - 180) x

Subtract the numbers

- 855 x

135 x^{2} - 855 x + 900

(135 x^{2} - 855 x + 900) x^{2}

Apply the distributive property

135 x^{2} \times x^{2} - 855 x \times x^{2} + 900 x^{2}

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{2}

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

x^{2 + 2}

Add the numbers

x^{4}

135 x^{4} - 855 x \times x^{2} + 900 x^{2}

Solution

More Steps

Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

135 x^{4} - 855 x^{3} + 900 x^{2}

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = 0, x_{2} = \frac{4}{3}, x_{3} = 5

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}, x_{3} = 5

Evaluate

(3 x - 4) (x - 5) (x \times 1) (3 x \times 15)

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

(3 x - 4) (x - 5) (x \times 1) (3 x \times 15) = 0

Any expression multiplied by 1 remains the same

(3 x - 4) (x - 5) x (3 x \times 15) = 0

Multiply the terms

(3 x - 4) (x - 5) x \times 45 x = 0

Multiply the terms

More Steps

Multiply the terms

(3 x - 4) (x - 5) x \times 45 x

Multiply the terms

(3 x - 4) (x - 5) x^{2} \times 45

Use the commutative property to reorder the terms

(3 x - 4) (x - 5) \times 45 x^{2}

Use the commutative property to reorder the terms

45 (3 x - 4) (x - 5) x^{2}

45 (3 x - 4) (x - 5) x^{2} = 0

Elimination the left coefficient

(3 x - 4) (x - 5) x^{2} = 0

Separate the equation into 3 possible cases

3 x - 4 = 0 x - 5 = 0 x^{2} = 0

Solve the equation

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = \frac{4}{3} x - 5 = 0 x^{2} = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = \frac{4}{3} x = 5 x^{2} = 0

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

x = \frac{4}{3} x = 5 x = 0

Solution

x_{1} = 0, x_{2} = \frac{4}{3}, x_{3} = 5

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}, x_{3} = 5

Show Solution

(3x 4)(x 5) (x 1)(3x 15)

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression