Solve (4q-2)(q-1)

Question

Simplify the expression

4 q^{2} - 6 q + 2

Evaluate

(4 q - 2) (q - 1)

Apply the distributive property

4 q \times q - 4 q \times 1 - 2 q - (- 2 \times 1)

Multiply the terms

4 q^{2} - 4 q \times 1 - 2 q - (- 2 \times 1)

Any expression multiplied by 1 remains the same

4 q^{2} - 4 q - 2 q - (- 2 \times 1)

Any expression multiplied by 1 remains the same

4 q^{2} - 4 q - 2 q - (- 2)

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

4 q^{2} - 4 q - 2 q + 2

Solution

More Steps

Evaluate

- 4 q - 2 q

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

(- 4 - 2) q

Subtract the numbers

- 6 q

4 q^{2} - 6 q + 2

Show Solution

Factor the expression

2 (2 q - 1) (q - 1)

Evaluate

(4 q - 2) (q - 1)

Solution

2 (2 q - 1) (q - 1)

Show Solution

Find the roots

q_{1} = \frac{1}{2}, q_{2} = 1

Alternative Form

q_{1} = 0.5, q_{2} = 1

Evaluate

(4 q - 2) (q - 1)

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

(4 q - 2) (q - 1) = 0

Separate the equation into 2 possible cases

4 q - 2 = 0 q - 1 = 0

Solve the equation

More Steps

Evaluate

4 q - 2 = 0

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

4 q = 0 + 2

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

4 q = 2

Divide both sides

\frac{4 q}{4} = \frac{2}{4}

Divide the numbers

q = \frac{2}{4}

Cancel out the common factor 2

q = \frac{1}{2}

q = \frac{1}{2} q - 1 = 0

Solve the equation

More Steps

Evaluate

q - 1 = 0

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

q = 0 + 1

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

q = 1

q = \frac{1}{2} q = 1

Solution

q_{1} = \frac{1}{2}, q_{2} = 1

Alternative Form

q_{1} = 0.5, q_{2} = 1

Show Solution