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

Question

Simplify the expression

10 x^{3} - 43 x^{2} + 42 x

Evaluate

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

Multiply the terms

(2 x - 3) (5 x^{2} - 14 x)

Apply the distributive property

2 x \times 5 x^{2} - 2 x \times 14 x - 3 \times 5 x^{2} - (- 3 \times 14 x)

Multiply the terms

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Evaluate

2 x \times 5 x^{2}

Multiply the numbers

10 x \times x^{2}

Multiply the terms

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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}

10 x^{3}

10 x^{3} - 2 x \times 14 x - 3 \times 5 x^{2} - (- 3 \times 14 x)

Multiply the terms

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Evaluate

2 x \times 14 x

Multiply the numbers

28 x \times x

Multiply the terms

28 x^{2}

10 x^{3} - 28 x^{2} - 3 \times 5 x^{2} - (- 3 \times 14 x)

Multiply the numbers

10 x^{3} - 28 x^{2} - 15 x^{2} - (- 3 \times 14 x)

Multiply the numbers

10 x^{3} - 28 x^{2} - 15 x^{2} - (- 42 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

10 x^{3} - 28 x^{2} - 15 x^{2} + 42 x

Solution

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Evaluate

- 28 x^{2} - 15 x^{2}

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

(- 28 - 15) x^{2}

Subtract the numbers

- 43 x^{2}

10 x^{3} - 43 x^{2} + 42 x

Show Solution

Factor the expression

x (2 x - 3) (5 x - 14)

Evaluate

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

Multiply the terms

(2 x - 3) (5 x^{2} - 14 x)

Factor the expression

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Evaluate

5 x^{2} - 14 x

Rewrite the expression

x \times 5 x - x \times 14

Factor out x from the expression

x (5 x - 14)

(2 x - 3) x (5 x - 14)

Solution

x (2 x - 3) (5 x - 14)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3}{2}, x_{3} = \frac{14}{5}

Alternative Form

x_{1} = 0, x_{2} = 1.5, x_{3} = 2.8

Evaluate

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

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

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

Multiply the terms

(2 x - 3) (5 x^{2} - 14 x) = 0

Separate the equation into 2 possible cases

2 x - 3 = 0 5 x^{2} - 14 x = 0

Solve the equation

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Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 5 x^{2} - 14 x = 0

Solve the equation

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Evaluate

5 x^{2} - 14 x = 0

Factor the expression

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Evaluate

5 x^{2} - 14 x

Rewrite the expression

x \times 5 x - x \times 14

Factor out x from the expression

x (5 x - 14)

x (5 x - 14) = 0

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

x = 0 5 x - 14 = 0

Solve the equation for x

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Evaluate

5 x - 14 = 0

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

5 x = 0 + 14

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

5 x = 14

Divide both sides

\frac{5 x}{5} = \frac{14}{5}

Divide the numbers

x = \frac{14}{5}

x = 0 x = \frac{14}{5}

x = \frac{3}{2} x = 0 x = \frac{14}{5}

Solution

x_{1} = 0, x_{2} = \frac{3}{2}, x_{3} = \frac{14}{5}

Alternative Form

x_{1} = 0, x_{2} = 1.5, x_{3} = 2.8

Show Solution