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

Question

Simplify the expression

2 d^{2} - 7 d + 6

Evaluate

(d - 2) (2 d - 3)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

d \times 2 d

Use the commutative property to reorder the terms

2 d \times d

Multiply the terms

2 d^{2}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

2 d^{2} - 3 d - 4 d - (- 2 \times 3)

Multiply the numbers

2 d^{2} - 3 d - 4 d - (- 6)

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} - 3 d - 4 d + 6

Solution

More Steps

Evaluate

- 3 d - 4 d

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

(- 3 - 4) d

Subtract the numbers

- 7 d

2 d^{2} - 7 d + 6

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

(d - 2) (2 d - 3)

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

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

Separate the equation into 2 possible cases

d - 2 = 0 2 d - 3 = 0

Solve the equation

More Steps

Evaluate

d - 2 = 0

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

d = 0 + 2

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

d = 2

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

Solution

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

Alternative Form

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

Show Solution