Solve (4d - 3)(2d - 1)

Question

Simplify the expression

8 d^{2} - 10 d + 3

Evaluate

(4 d - 3) (2 d - 1)

Apply the distributive property

4 d \times 2 d - 4 d \times 1 - 3 \times 2 d - (- 3 \times 1)

Multiply the terms

More Steps

Evaluate

4 d \times 2 d

Multiply the numbers

8 d \times d

Multiply the terms

8 d^{2}

8 d^{2} - 4 d \times 1 - 3 \times 2 d - (- 3 \times 1)

Any expression multiplied by 1 remains the same

8 d^{2} - 4 d - 3 \times 2 d - (- 3 \times 1)

Multiply the numbers

8 d^{2} - 4 d - 6 d - (- 3 \times 1)

Any expression multiplied by 1 remains the same

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

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

8 d^{2} - 4 d - 6 d + 3

Solution

More Steps

Evaluate

- 4 d - 6 d

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

(- 4 - 6) d

Subtract the numbers

- 10 d

8 d^{2} - 10 d + 3

Show Solution

Find the roots

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

Alternative Form

d_{1} = 0.5, d_{2} = 0.75

Evaluate

(4 d - 3) (2 d - 1)

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

(4 d - 3) (2 d - 1) = 0

Separate the equation into 2 possible cases

4 d - 3 = 0 2 d - 1 = 0

Solve the equation

More Steps

Evaluate

4 d - 3 = 0

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

4 d = 0 + 3

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

4 d = 3

Divide both sides

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

Divide the numbers

d = \frac{3}{4}

d = \frac{3}{4} 2 d - 1 = 0

Solve the equation

More Steps

Evaluate

2 d - 1 = 0

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

2 d = 0 + 1

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

2 d = 1

Divide both sides

\frac{2 d}{2} = \frac{1}{2}

Divide the numbers

d = \frac{1}{2}

d = \frac{3}{4} d = \frac{1}{2}

Solution

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

Alternative Form

d_{1} = 0.5, d_{2} = 0.75

Show Solution