Solve (2x^2 - 5x 7)(3x - 2)

Question

Simplify the expression

6 x^{3} - 109 x^{2} + 70 x

Evaluate

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

Multiply the terms

(2 x^{2} - 35 x) (3 x - 2)

Apply the distributive property

2 x^{2} \times 3 x - 2 x^{2} \times 2 - 35 x \times 3 x - (- 35 x \times 2)

Multiply the terms

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Evaluate

2 x^{2} \times 3 x

Multiply the numbers

6 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}

6 x^{3}

6 x^{3} - 2 x^{2} \times 2 - 35 x \times 3 x - (- 35 x \times 2)

Multiply the numbers

6 x^{3} - 4 x^{2} - 35 x \times 3 x - (- 35 x \times 2)

Multiply the terms

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Evaluate

- 35 x \times 3 x

Multiply the numbers

- 105 x \times x

Multiply the terms

- 105 x^{2}

6 x^{3} - 4 x^{2} - 105 x^{2} - (- 35 x \times 2)

Multiply the numbers

6 x^{3} - 4 x^{2} - 105 x^{2} - (- 70 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

6 x^{3} - 4 x^{2} - 105 x^{2} + 70 x

Solution

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Evaluate

- 4 x^{2} - 105 x^{2}

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

(- 4 - 105) x^{2}

Subtract the numbers

- 109 x^{2}

6 x^{3} - 109 x^{2} + 70 x

Show Solution

Factor the expression

x (2 x - 35) (3 x - 2)

Evaluate

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

Multiply the terms

(2 x^{2} - 35 x) (3 x - 2)

Solution

More Steps

Evaluate

2 x^{2} - 35 x

Rewrite the expression

x \times 2 x - x \times 35

Factor out x from the expression

x (2 x - 35)

x (2 x - 35) (3 x - 2)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{2}{3}, x_{3} = \frac{35}{2}

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{6}, x_{3} = 17.5

Evaluate

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

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

(2 x^{2} - 5 x \times 7) (3 x - 2) = 0

Multiply the terms

(2 x^{2} - 35 x) (3 x - 2) = 0

Separate the equation into 2 possible cases

2 x^{2} - 35 x = 0 3 x - 2 = 0

Solve the equation

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Evaluate

2 x^{2} - 35 x = 0

Factor the expression

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Evaluate

2 x^{2} - 35 x

Rewrite the expression

x \times 2 x - x \times 35

Factor out x from the expression

x (2 x - 35)

x (2 x - 35) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 2 x - 35 = 0

Solve the equation for x

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Evaluate

2 x - 35 = 0

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

2 x = 0 + 35

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

2 x = 35

Divide both sides

\frac{2 x}{2} = \frac{35}{2}

Divide the numbers

x = \frac{35}{2}

x = 0 x = \frac{35}{2}

x = 0 x = \frac{35}{2} 3 x - 2 = 0

Solve the equation

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Evaluate

3 x - 2 = 0

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

3 x = 0 + 2

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

3 x = 2

Divide both sides

\frac{3 x}{3} = \frac{2}{3}

Divide the numbers

x = \frac{2}{3}

x = 0 x = \frac{35}{2} x = \frac{2}{3}

Solution

x_{1} = 0, x_{2} = \frac{2}{3}, x_{3} = \frac{35}{2}

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{6}, x_{3} = 17.5

Show Solution