Solve x (7x-5) (3x-3)

Question

Simplify the expression

21 x^{3} - 36 x^{2} + 15 x

Evaluate

x (7 x - 5) (3 x - 3)

Multiply the terms

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Evaluate

x (7 x - 5)

Apply the distributive property

x \times 7 x - x \times 5

Multiply the terms

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Evaluate

x \times 7 x

Use the commutative property to reorder the terms

7 x \times x

Multiply the terms

7 x^{2}

7 x^{2} - x \times 5

Use the commutative property to reorder the terms

7 x^{2} - 5 x

(7 x^{2} - 5 x) (3 x - 3)

Apply the distributive property

7 x^{2} \times 3 x - 7 x^{2} \times 3 - 5 x \times 3 x - (- 5 x \times 3)

Multiply the terms

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Evaluate

7 x^{2} \times 3 x

Multiply the numbers

21 x^{2} \times x

Multiply the terms

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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}

21 x^{3}

21 x^{3} - 7 x^{2} \times 3 - 5 x \times 3 x - (- 5 x \times 3)

Multiply the numbers

21 x^{3} - 21 x^{2} - 5 x \times 3 x - (- 5 x \times 3)

Multiply the terms

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Evaluate

- 5 x \times 3 x

Multiply the numbers

- 15 x \times x

Multiply the terms

- 15 x^{2}

21 x^{3} - 21 x^{2} - 15 x^{2} - (- 5 x \times 3)

Multiply the numbers

21 x^{3} - 21 x^{2} - 15 x^{2} - (- 15 x)

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

21 x^{3} - 21 x^{2} - 15 x^{2} + 15 x

Solution

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Evaluate

- 21 x^{2} - 15 x^{2}

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

(- 21 - 15) x^{2}

Subtract the numbers

- 36 x^{2}

21 x^{3} - 36 x^{2} + 15 x

Show Solution

Factor the expression

3 x (7 x - 5) (x - 1)

Evaluate

x (7 x - 5) (3 x - 3)

Factor the expression

x (7 x - 5) \times 3 (x - 1)

Solution

3 x (7 x - 5) (x - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5}{7}, x_{3} = 1

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{7} 1428 \dot{5}, x_{3} = 1

Evaluate

x (7 x - 5) (3 x - 3)

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

x (7 x - 5) (3 x - 3) = 0

Separate the equation into 3 possible cases

x = 0 7 x - 5 = 0 3 x - 3 = 0

Solve the equation

More Steps

Evaluate

7 x - 5 = 0

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

7 x = 0 + 5

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

7 x = 5

Divide both sides

\frac{7 x}{7} = \frac{5}{7}

Divide the numbers

x = \frac{5}{7}

x = 0 x = \frac{5}{7} 3 x - 3 = 0

Solve the equation

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Evaluate

3 x - 3 = 0

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

3 x = 0 + 3

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

3 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{3}

Divide the numbers

More Steps

Evaluate

\frac{3}{3}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

x = 0 x = \frac{5}{7} x = 1

Solution

x_{1} = 0, x_{2} = \frac{5}{7}, x_{3} = 1

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{7} 1428 \dot{5}, x_{3} = 1

Show Solution