Solve b-2/3b 15 b-1/3b 15

Question

Simplify the expression

- 4 b - 10 b^{2}

Evaluate

b - \frac{2}{3} b \times 15 b - \frac{1}{3} b \times 15

Multiply

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Multiply the terms

- \frac{2}{3} b \times 15 b

Multiply the terms

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Evaluate

\frac{2}{3} \times 15

Reduce the numbers

2 \times 5

Multiply the numbers

10

- 10 b \times b

Multiply the terms

- 10 b^{2}

b - 10 b^{2} - \frac{1}{3} b \times 15

Multiply the terms

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Multiply the terms

- \frac{1}{3} b \times 15

Multiply the terms

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Evaluate

\frac{1}{3} \times 15

Reduce the numbers

1 \times 5

Simplify

5

- 5 b

b - 10 b^{2} - 5 b

Solution

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Evaluate

b - 5 b

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

(1 - 5) b

Subtract the numbers

- 4 b

- 4 b - 10 b^{2}

Show Solution

Factor the expression

- 2 b (2 + 5 b)

Evaluate

b - \frac{2}{3} b \times 15 b - \frac{1}{3} b \times 15

Multiply

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Multiply the terms

\frac{2}{3} b \times 15 b

Multiply the terms

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Evaluate

\frac{2}{3} \times 15

Reduce the numbers

2 \times 5

Multiply the numbers

10

10 b \times b

Multiply the terms

10 b^{2}

b - 10 b^{2} - \frac{1}{3} b \times 15

Multiply the terms

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Multiply the terms

\frac{1}{3} b \times 15

Multiply the terms

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Evaluate

\frac{1}{3} \times 15

Reduce the numbers

1 \times 5

Simplify

5

5 b

b - 10 b^{2} - 5 b

Subtract the terms

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Evaluate

b - 5 b

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

(1 - 5) b

Subtract the numbers

- 4 b

- 4 b - 10 b^{2}

Rewrite the expression

- 2 b \times 2 - 2 b \times 5 b

Solution

- 2 b (2 + 5 b)

Show Solution

Find the roots

b_{1} = - \frac{2}{5}, b_{2} = 0

Alternative Form

b_{1} = - 0.4, b_{2} = 0

Evaluate

b - \frac{2}{3} b \times 15 b - \frac{1}{3} b \times 15

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

b - \frac{2}{3} b \times 15 b - \frac{1}{3} b \times 15 = 0

Multiply

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Multiply the terms

\frac{2}{3} b \times 15 b

Multiply the terms

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Evaluate

\frac{2}{3} \times 15

Reduce the numbers

2 \times 5

Multiply the numbers

10

10 b \times b

Multiply the terms

10 b^{2}

b - 10 b^{2} - \frac{1}{3} b \times 15 = 0

Multiply the terms

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Multiply the terms

\frac{1}{3} b \times 15

Multiply the terms

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Evaluate

\frac{1}{3} \times 15

Reduce the numbers

1 \times 5

Simplify

5

5 b

b - 10 b^{2} - 5 b = 0

Subtract the terms

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Simplify

b - 10 b^{2} - 5 b

Subtract the terms

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Evaluate

b - 5 b

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

(1 - 5) b

Subtract the numbers

- 4 b

- 4 b - 10 b^{2}

- 4 b - 10 b^{2} = 0

Factor the expression

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Evaluate

- 4 b - 10 b^{2}

Rewrite the expression

- 2 b \times 2 - 2 b \times 5 b

Factor out - 2 b from the expression

- 2 b (2 + 5 b)

- 2 b (2 + 5 b) = 0

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

- 2 b = 0 2 + 5 b = 0

Solve the equation for b

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Evaluate

- 2 b = 0

Change the signs on both sides of the equation

2 b = 0

Rewrite the expression

b = 0

b = 0 2 + 5 b = 0

Solve the equation for b

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Evaluate

2 + 5 b = 0

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

5 b = 0 - 2

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

5 b = - 2

Divide both sides

\frac{5 b}{5} = \frac{- 2}{5}

Divide the numbers

b = \frac{- 2}{5}

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

b = - \frac{2}{5}

b = 0 b = - \frac{2}{5}

Solution

b_{1} = - \frac{2}{5}, b_{2} = 0

Alternative Form

b_{1} = - 0.4, b_{2} = 0

Show Solution