Solve 2(4y - 10) 3(-2y - 3)

Question

Simplify the expression

- 48 y^{2} + 48 y + 180

Evaluate

2 (4 y - 10) \times 3 (- 2 y - 3)

Multiply the terms

6 (4 y - 10) (- 2 y - 3)

Multiply the terms

More Steps

Evaluate

6 (4 y - 10)

Apply the distributive property

6 \times 4 y - 6 \times 10

Multiply the numbers

24 y - 6 \times 10

Multiply the numbers

24 y - 60

(24 y - 60) (- 2 y - 3)

Apply the distributive property

24 y (- 2 y) - 24 y \times 3 - 60 (- 2 y) - (- 60 \times 3)

Multiply the terms

More Steps

Evaluate

24 y (- 2 y)

Multiply the numbers

More Steps

Evaluate

24 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 24 \times 2

Multiply the numbers

- 48

- 48 y \times y

Multiply the terms

- 48 y^{2}

- 48 y^{2} - 24 y \times 3 - 60 (- 2 y) - (- 60 \times 3)

Multiply the numbers

- 48 y^{2} - 72 y - 60 (- 2 y) - (- 60 \times 3)

Multiply the numbers

More Steps

Evaluate

- 60 (- 2)

Multiplying or dividing an even number of negative terms equals a positive

60 \times 2

Multiply the numbers

120

- 48 y^{2} - 72 y + 120 y - (- 60 \times 3)

Multiply the numbers

- 48 y^{2} - 72 y + 120 y - (- 180)

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

- 48 y^{2} - 72 y + 120 y + 180

Solution

More Steps

Evaluate

- 72 y + 120 y

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

(- 72 + 120) y

Add the numbers

48 y

- 48 y^{2} + 48 y + 180

Show Solution

Factor the expression

- 12 (2 y - 5) (2 y + 3)

Evaluate

2 (4 y - 10) \times 3 (- 2 y - 3)

Multiply the terms

6 (4 y - 10) (- 2 y - 3)

Factor the expression

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

Factor the expression

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

Solution

- 12 (2 y - 5) (2 y + 3)

Show Solution

Find the roots

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

Alternative Form

y_{1} = - 1.5, y_{2} = 2.5

Evaluate

2 (4 y - 10) \times 3 (- 2 y - 3)

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

2 (4 y - 10) \times 3 (- 2 y - 3) = 0

Multiply the terms

6 (4 y - 10) (- 2 y - 3) = 0

Elimination the left coefficient

(4 y - 10) (- 2 y - 3) = 0

Separate the equation into 2 possible cases

4 y - 10 = 0 - 2 y - 3 = 0

Solve the equation

More Steps

Evaluate

4 y - 10 = 0

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

4 y = 0 + 10

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

4 y = 10

Divide both sides

\frac{4 y}{4} = \frac{10}{4}

Divide the numbers

y = \frac{10}{4}

Cancel out the common factor 2

y = \frac{5}{2}

y = \frac{5}{2} - 2 y - 3 = 0

Solve the equation

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

Change the signs on both sides of the equation

2 y = - 3

Divide both sides

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

Divide the numbers

y = \frac{- 3}{2}

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

y = - \frac{3}{2}

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

Solution

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

Alternative Form

y_{1} = - 1.5, y_{2} = 2.5

Show Solution