Solve (4y-5)(6y-5)

Question

Simplify the expression

24 y^{2} - 50 y + 25

Evaluate

(4 y - 5) (6 y - 5)

Apply the distributive property

4 y \times 6 y - 4 y \times 5 - 5 \times 6 y - (- 5 \times 5)

Multiply the terms

More Steps

Evaluate

4 y \times 6 y

Multiply the numbers

24 y \times y

Multiply the terms

24 y^{2}

24 y^{2} - 4 y \times 5 - 5 \times 6 y - (- 5 \times 5)

Multiply the numbers

24 y^{2} - 20 y - 5 \times 6 y - (- 5 \times 5)

Multiply the numbers

24 y^{2} - 20 y - 30 y - (- 5 \times 5)

Multiply the numbers

24 y^{2} - 20 y - 30 y - (- 25)

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

24 y^{2} - 20 y - 30 y + 25

Solution

More Steps

Evaluate

- 20 y - 30 y

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

(- 20 - 30) y

Subtract the numbers

- 50 y

24 y^{2} - 50 y + 25

Show Solution

Find the roots

y_{1} = \frac{5}{6}, y_{2} = \frac{5}{4}

Alternative Form

y_{1} = 0.8 \dot{3}, y_{2} = 1.25

Evaluate

(4 y - 5) (6 y - 5)

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

(4 y - 5) (6 y - 5) = 0

Separate the equation into 2 possible cases

4 y - 5 = 0 6 y - 5 = 0

Solve the equation

More Steps

Evaluate

4 y - 5 = 0

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

4 y = 0 + 5

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

4 y = 5

Divide both sides

\frac{4 y}{4} = \frac{5}{4}

Divide the numbers

y = \frac{5}{4}

y = \frac{5}{4} 6 y - 5 = 0

Solve the equation

More Steps

Evaluate

6 y - 5 = 0

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

6 y = 0 + 5

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

6 y = 5

Divide both sides

\frac{6 y}{6} = \frac{5}{6}

Divide the numbers

y = \frac{5}{6}

y = \frac{5}{4} y = \frac{5}{6}

Solution

y_{1} = \frac{5}{6}, y_{2} = \frac{5}{4}

Alternative Form

y_{1} = 0.8 \dot{3}, y_{2} = 1.25

Show Solution