Solve (y 9)(y-3)-4y(2-3y)

Question

Simplify the expression

21 y^{2} - 35 y

Evaluate

(y \times 9) (y - 3) - 4 y (2 - 3 y)

Remove the parentheses

y \times 9 (y - 3) - 4 y (2 - 3 y)

Use the commutative property to reorder the terms

9 y (y - 3) - 4 y (2 - 3 y)

Expand the expression

More Steps

Calculate

9 y (y - 3)

Apply the distributive property

9 y \times y - 9 y \times 3

Multiply the terms

9 y^{2} - 9 y \times 3

Multiply the numbers

9 y^{2} - 27 y

9 y^{2} - 27 y - 4 y (2 - 3 y)

Expand the expression

More Steps

Calculate

- 4 y (2 - 3 y)

Apply the distributive property

- 4 y \times 2 - (- 4 y \times 3 y)

Multiply the numbers

- 8 y - (- 4 y \times 3 y)

Multiply the terms

More Steps

Evaluate

- 4 y \times 3 y

Multiply the numbers

- 12 y \times y

Multiply the terms

- 12 y^{2}

- 8 y - (- 12 y^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 y + 12 y^{2}

9 y^{2} - 27 y - 8 y + 12 y^{2}

Add the terms

More Steps

Evaluate

9 y^{2} + 12 y^{2}

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

(9 + 12) y^{2}

Add the numbers

21 y^{2}

21 y^{2} - 27 y - 8 y

Solution

More Steps

Evaluate

- 27 y - 8 y

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

(- 27 - 8) y

Subtract the numbers

- 35 y

21 y^{2} - 35 y

Show Solution

Factor the expression

7 y (3 y - 5)

Evaluate

(y \times 9) (y - 3) - 4 y (2 - 3 y)

Remove the parentheses

y \times 9 (y - 3) - 4 y (2 - 3 y)

Use the commutative property to reorder the terms

9 y (y - 3) - 4 y (2 - 3 y)

Rewrite the expression

9 (y - 3) y - 4 (2 - 3 y) y

Factor out y from the expression

(9 (y - 3) - 4 (2 - 3 y)) y

Factor the expression

More Steps

Evaluate

9 (y - 3) - 4 (2 - 3 y)

Simplify

More Steps

Evaluate

9 (y - 3)

Apply the distributive property

9 y + 9 (- 3)

Multiply the terms

9 y - 27

9 y - 27 - 4 (2 - 3 y)

Simplify

More Steps

Evaluate

- 4 (2 - 3 y)

Apply the distributive property

- 4 \times 2 - 4 (- 3 y)

Multiply the terms

- 8 - 4 (- 3 y)

Multiply the terms

- 8 + 12 y

9 y - 27 - 8 + 12 y

Add the terms

More Steps

Evaluate

9 y + 12 y

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

(9 + 12) y

Add the numbers

21 y

21 y - 27 - 8

Subtract the numbers

21 y - 35

Factor the expression

7 (3 y - 5)

7 (3 y - 5) y

Solution

7 y (3 y - 5)

Show Solution

Find the roots

y_{1} = 0, y_{2} = \frac{5}{3}

Alternative Form

y_{1} = 0, y_{2} = 1. \dot{6}

Evaluate

(y \times 9) (y - 3) - 4 y (2 - 3 y)

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

(y \times 9) (y - 3) - 4 y (2 - 3 y) = 0

Use the commutative property to reorder the terms

9 y (y - 3) - 4 y (2 - 3 y) = 0

Calculate

More Steps

Evaluate

9 y (y - 3) - 4 y (2 - 3 y)

Expand the expression

More Steps

Calculate

9 y (y - 3)

Apply the distributive property

9 y \times y - 9 y \times 3

Multiply the terms

9 y^{2} - 9 y \times 3

Multiply the numbers

9 y^{2} - 27 y

9 y^{2} - 27 y - 4 y (2 - 3 y)

Expand the expression

More Steps

Calculate

- 4 y (2 - 3 y)

Apply the distributive property

- 4 y \times 2 - (- 4 y \times 3 y)

Multiply the numbers

- 8 y - (- 4 y \times 3 y)

Multiply the terms

- 8 y - (- 12 y^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 y + 12 y^{2}

9 y^{2} - 27 y - 8 y + 12 y^{2}

Add the terms

More Steps

Evaluate

9 y^{2} + 12 y^{2}

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

(9 + 12) y^{2}

Add the numbers

21 y^{2}

21 y^{2} - 27 y - 8 y

Subtract the terms

More Steps

Evaluate

- 27 y - 8 y

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

(- 27 - 8) y

Subtract the numbers

- 35 y

21 y^{2} - 35 y

21 y^{2} - 35 y = 0

Factor the expression

More Steps

Evaluate

21 y^{2} - 35 y

Rewrite the expression

7 y \times 3 y - 7 y \times 5

Factor out 7 y from the expression

7 y (3 y - 5)

7 y (3 y - 5) = 0

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

7 y = 0 3 y - 5 = 0

Solve the equation for y

y = 0 3 y - 5 = 0

Solve the equation for y

More Steps

Evaluate

3 y - 5 = 0

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

3 y = 0 + 5

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

3 y = 5

Divide both sides

\frac{3 y}{3} = \frac{5}{3}

Divide the numbers

y = \frac{5}{3}

y = 0 y = \frac{5}{3}

Solution

y_{1} = 0, y_{2} = \frac{5}{3}

Alternative Form

y_{1} = 0, y_{2} = 1. \dot{6}

Show Solution