Solve (9d -4) (4d -6)

Question

Simplify the expression

36 d^{2} - 70 d + 24

Evaluate

(9 d - 4) (4 d - 6)

Apply the distributive property

9 d \times 4 d - 9 d \times 6 - 4 \times 4 d - (- 4 \times 6)

Multiply the terms

More Steps

Evaluate

9 d \times 4 d

Multiply the numbers

36 d \times d

Multiply the terms

36 d^{2}

36 d^{2} - 9 d \times 6 - 4 \times 4 d - (- 4 \times 6)

Multiply the numbers

36 d^{2} - 54 d - 4 \times 4 d - (- 4 \times 6)

Multiply the numbers

36 d^{2} - 54 d - 16 d - (- 4 \times 6)

Multiply the numbers

36 d^{2} - 54 d - 16 d - (- 24)

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

36 d^{2} - 54 d - 16 d + 24

Solution

More Steps

Evaluate

- 54 d - 16 d

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

(- 54 - 16) d

Subtract the numbers

- 70 d

36 d^{2} - 70 d + 24

Show Solution

Factor the expression

2 (9 d - 4) (2 d - 3)

Evaluate

(9 d - 4) (4 d - 6)

Factor the expression

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

Solution

2 (9 d - 4) (2 d - 3)

Show Solution

Find the roots

d_{1} = \frac{4}{9}, d_{2} = \frac{3}{2}

Alternative Form

d_{1} = 0. \dot{4}, d_{2} = 1.5

Evaluate

(9 d - 4) (4 d - 6)

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

(9 d - 4) (4 d - 6) = 0

Separate the equation into 2 possible cases

9 d - 4 = 0 4 d - 6 = 0

Solve the equation

More Steps

Evaluate

9 d - 4 = 0

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

9 d = 0 + 4

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

9 d = 4

Divide both sides

\frac{9 d}{9} = \frac{4}{9}

Divide the numbers

d = \frac{4}{9}

d = \frac{4}{9} 4 d - 6 = 0

Solve the equation

More Steps

Evaluate

4 d - 6 = 0

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

4 d = 0 + 6

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

4 d = 6

Divide both sides

\frac{4 d}{4} = \frac{6}{4}

Divide the numbers

d = \frac{6}{4}

Cancel out the common factor 2

d = \frac{3}{2}

d = \frac{4}{9} d = \frac{3}{2}

Solution

d_{1} = \frac{4}{9}, d_{2} = \frac{3}{2}

Alternative Form

d_{1} = 0. \dot{4}, d_{2} = 1.5

Show Solution