Solve (3w - 7)(2w - 1)

Question

Simplify the expression

6 w^{2} - 17 w + 7

Evaluate

(3 w - 7) (2 w - 1)

Apply the distributive property

3 w \times 2 w - 3 w \times 1 - 7 \times 2 w - (- 7 \times 1)

Multiply the terms

More Steps

Evaluate

3 w \times 2 w

Multiply the numbers

6 w \times w

Multiply the terms

6 w^{2}

6 w^{2} - 3 w \times 1 - 7 \times 2 w - (- 7 \times 1)

Any expression multiplied by 1 remains the same

6 w^{2} - 3 w - 7 \times 2 w - (- 7 \times 1)

Multiply the numbers

6 w^{2} - 3 w - 14 w - (- 7 \times 1)

Any expression multiplied by 1 remains the same

6 w^{2} - 3 w - 14 w - (- 7)

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

6 w^{2} - 3 w - 14 w + 7

Solution

More Steps

Evaluate

- 3 w - 14 w

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

(- 3 - 14) w

Subtract the numbers

- 17 w

6 w^{2} - 17 w + 7

Show Solution

Find the roots

w_{1} = \frac{1}{2}, w_{2} = \frac{7}{3}

Alternative Form

w_{1} = 0.5, w_{2} = 2. \dot{3}

Evaluate

(3 w - 7) (2 w - 1)

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

(3 w - 7) (2 w - 1) = 0

Separate the equation into 2 possible cases

3 w - 7 = 0 2 w - 1 = 0

Solve the equation

More Steps

Evaluate

3 w - 7 = 0

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

3 w = 0 + 7

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

3 w = 7

Divide both sides

\frac{3 w}{3} = \frac{7}{3}

Divide the numbers

w = \frac{7}{3}

w = \frac{7}{3} 2 w - 1 = 0

Solve the equation

More Steps

Evaluate

2 w - 1 = 0

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

2 w = 0 + 1

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

2 w = 1

Divide both sides

\frac{2 w}{2} = \frac{1}{2}

Divide the numbers

w = \frac{1}{2}

w = \frac{7}{3} w = \frac{1}{2}

Solution

w_{1} = \frac{1}{2}, w_{2} = \frac{7}{3}

Alternative Form

w_{1} = 0.5, w_{2} = 2. \dot{3}

Show Solution