Solve 5y(2y-3)+(2y-3)

Question

Simplify the expression

10 y^{2} - 13 y - 3

Evaluate

5 y (2 y - 3) + (2 y - 3)

Remove the parentheses

5 y (2 y - 3) + 2 y - 3

Expand the expression

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Calculate

5 y (2 y - 3)

Apply the distributive property

5 y \times 2 y - 5 y \times 3

Multiply the terms

More Steps

Evaluate

5 y \times 2 y

Multiply the numbers

10 y \times y

Multiply the terms

10 y^{2}

10 y^{2} - 5 y \times 3

Multiply the numbers

10 y^{2} - 15 y

10 y^{2} - 15 y + 2 y - 3

Solution

More Steps

Evaluate

- 15 y + 2 y

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

(- 15 + 2) y

Add the numbers

- 13 y

10 y^{2} - 13 y - 3

Show Solution

Factor the expression

(2 y - 3) (5 y + 1)

Evaluate

5 y (2 y - 3) + (2 y - 3)

Remove the parentheses

5 y (2 y - 3) + 2 y - 3

Rewrite the expression

(2 y - 3) \times 5 y + 2 y - 3

Solution

(2 y - 3) (5 y + 1)

Show Solution

Find the roots

y_{1} = - \frac{1}{5}, y_{2} = \frac{3}{2}

Alternative Form

y_{1} = - 0.2, y_{2} = 1.5

Evaluate

5 y (2 y - 3) + (2 y - 3)

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

5 y (2 y - 3) + (2 y - 3) = 0

Remove the parentheses

5 y (2 y - 3) + 2 y - 3 = 0

Calculate the sum or difference

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Evaluate

5 y (2 y - 3) + 2 y - 3

Expand the expression

More Steps

Calculate

5 y (2 y - 3)

Apply the distributive property

5 y \times 2 y - 5 y \times 3

Multiply the terms

10 y^{2} - 5 y \times 3

Multiply the numbers

10 y^{2} - 15 y

10 y^{2} - 15 y + 2 y - 3

Add the terms

More Steps

Evaluate

- 15 y + 2 y

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

(- 15 + 2) y

Add the numbers

- 13 y

10 y^{2} - 13 y - 3

10 y^{2} - 13 y - 3 = 0

Factor the expression

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Evaluate

10 y^{2} - 13 y - 3

Rewrite the expression

10 y^{2} + (2 - 15) y - 3

Calculate

10 y^{2} + 2 y - 15 y - 3

Rewrite the expression

2 y \times 5 y + 2 y - 3 \times 5 y - 3

Factor out 2 y from the expression

2 y (5 y + 1) - 3 \times 5 y - 3

Factor out - 3 from the expression

2 y (5 y + 1) - 3 (5 y + 1)

Factor out 5 y + 1 from the expression

(2 y - 3) (5 y + 1)

(2 y - 3) (5 y + 1) = 0

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

2 y - 3 = 0 5 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

2 y - 3 = 0

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

2 y = 0 + 3

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

2 y = 3

Divide both sides

\frac{2 y}{2} = \frac{3}{2}

Divide the numbers

y = \frac{3}{2}

y = \frac{3}{2} 5 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

5 y + 1 = 0

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

5 y = 0 - 1

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

5 y = - 1

Divide both sides

\frac{5 y}{5} = \frac{- 1}{5}

Divide the numbers

y = \frac{- 1}{5}

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

y = - \frac{1}{5}

y = \frac{3}{2} y = - \frac{1}{5}

Solution

y_{1} = - \frac{1}{5}, y_{2} = \frac{3}{2}

Alternative Form

y_{1} = - 0.2, y_{2} = 1.5

Show Solution