Solve 10y(6y+21)/5(2y+7)

Question

Simplify the expression

24 y^{3} + 168 y^{2} + 294 y

Evaluate

10 y \times \frac{6 y + 21}{5} \times (2 y + 7)

Cancel out the common factor 5

2 y (6 y + 21) (2 y + 7)

Multiply the terms

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Evaluate

2 y (6 y + 21)

Apply the distributive property

2 y \times 6 y + 2 y \times 21

Multiply the terms

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Evaluate

2 y \times 6 y

Multiply the numbers

12 y \times y

Multiply the terms

12 y^{2}

12 y^{2} + 2 y \times 21

Multiply the numbers

12 y^{2} + 42 y

(12 y^{2} + 42 y) (2 y + 7)

Apply the distributive property

12 y^{2} \times 2 y + 12 y^{2} \times 7 + 42 y \times 2 y + 42 y \times 7

Multiply the terms

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Evaluate

12 y^{2} \times 2 y

Multiply the numbers

24 y^{2} \times y

Multiply the terms

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Evaluate

y^{2} \times y

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

y^{2 + 1}

Add the numbers

y^{3}

24 y^{3}

24 y^{3} + 12 y^{2} \times 7 + 42 y \times 2 y + 42 y \times 7

Multiply the numbers

24 y^{3} + 84 y^{2} + 42 y \times 2 y + 42 y \times 7

Multiply the terms

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Evaluate

42 y \times 2 y

Multiply the numbers

84 y \times y

Multiply the terms

84 y^{2}

24 y^{3} + 84 y^{2} + 84 y^{2} + 42 y \times 7

Multiply the numbers

24 y^{3} + 84 y^{2} + 84 y^{2} + 294 y

Solution

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Evaluate

84 y^{2} + 84 y^{2}

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

(84 + 84) y^{2}

Add the numbers

168 y^{2}

24 y^{3} + 168 y^{2} + 294 y

Show Solution

Factor the expression

6 y (2 y + 7)^{2}

Evaluate

10 y \times \frac{6 y + 21}{5} \times (2 y + 7)

Cancel out the common factor 5

2 y (6 y + 21) (2 y + 7)

Factor the expression

2 y \times 3 (2 y + 7) (2 y + 7)

Solution

6 y (2 y + 7)^{2}

Show Solution

Find the roots

y_{1} = - \frac{7}{2}, y_{2} = 0

Alternative Form

y_{1} = - 3.5, y_{2} = 0

Evaluate

10 y \times \frac{6 y + 21}{5} \times (2 y + 7)

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

10 y \times \frac{6 y + 21}{5} \times (2 y + 7) = 0

Cancel out the common factor 5

2 y (6 y + 21) (2 y + 7) = 0

Elimination the left coefficient

y (6 y + 21) (2 y + 7) = 0

Separate the equation into 3 possible cases

y = 0 6 y + 21 = 0 2 y + 7 = 0

Solve the equation

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Evaluate

6 y + 21 = 0

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

6 y = 0 - 21

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

6 y = - 21

Divide both sides

\frac{6 y}{6} = \frac{- 21}{6}

Divide the numbers

y = \frac{- 21}{6}

Divide the numbers

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Evaluate

\frac{- 21}{6}

Cancel out the common factor 3

\frac{- 7}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{7}{2}

y = - \frac{7}{2}

y = 0 y = - \frac{7}{2} 2 y + 7 = 0

Solve the equation

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Evaluate

2 y + 7 = 0

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

2 y = 0 - 7

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

2 y = - 7

Divide both sides

\frac{2 y}{2} = \frac{- 7}{2}

Divide the numbers

y = \frac{- 7}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y = - \frac{7}{2}

y = 0 y = - \frac{7}{2} y = - \frac{7}{2}

Find the union

y = 0 y = - \frac{7}{2}

Solution

y_{1} = - \frac{7}{2}, y_{2} = 0

Alternative Form

y_{1} = - 3.5, y_{2} = 0

Show Solution