Solve (2d-3)(d-3)

Question

Simplify the expression

2 d^{2} - 9 d + 9

Evaluate

(2 d - 3) (d - 3)

Apply the distributive property

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

Multiply the terms

2 d^{2} - 2 d \times 3 - 3 d - (- 3 \times 3)

Multiply the numbers

2 d^{2} - 6 d - 3 d - (- 3 \times 3)

Multiply the numbers

2 d^{2} - 6 d - 3 d - (- 9)

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

2 d^{2} - 6 d - 3 d + 9

Solution

More Steps

Evaluate

- 6 d - 3 d

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

(- 6 - 3) d

Subtract the numbers

- 9 d

2 d^{2} - 9 d + 9

Show Solution

Find the roots

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

Alternative Form

d_{1} = 1.5, d_{2} = 3

Evaluate

(2 d - 3) (d - 3)

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

(2 d - 3) (d - 3) = 0

Separate the equation into 2 possible cases

2 d - 3 = 0 d - 3 = 0

Solve the equation

More Steps

Evaluate

2 d - 3 = 0

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

2 d = 0 + 3

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

2 d = 3

Divide both sides

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

Divide the numbers

d = \frac{3}{2}

d = \frac{3}{2} d - 3 = 0

Solve the equation

More Steps

Evaluate

d - 3 = 0

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

d = 0 + 3

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

d = 3

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

Solution

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

Alternative Form

d_{1} = 1.5, d_{2} = 3

Show Solution