Solve (3x -2)(2x-1)-1

Question

Simplify the expression

6 x^{2} - 7 x + 1

Evaluate

(3 x - 2) (2 x - 1) - 1

Expand the expression

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Calculate

(3 x - 2) (2 x - 1)

Apply the distributive property

3 x \times 2 x - 3 x \times 1 - 2 \times 2 x - (- 2 \times 1)

Multiply the terms

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Evaluate

3 x \times 2 x

Multiply the numbers

6 x \times x

Multiply the terms

6 x^{2}

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

Any expression multiplied by 1 remains the same

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

Multiply the numbers

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

Any expression multiplied by 1 remains the same

6 x^{2} - 3 x - 4 x - (- 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

6 x^{2} - 3 x - 4 x + 2

Subtract the terms

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Evaluate

- 3 x - 4 x

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

(- 3 - 4) x

Subtract the numbers

- 7 x

6 x^{2} - 7 x + 2

6 x^{2} - 7 x + 2 - 1

Solution

6 x^{2} - 7 x + 1

Show Solution

Factor the expression

(x - 1) (6 x - 1)

Evaluate

(3 x - 2) (2 x - 1) - 1

Simplify

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Evaluate

(3 x - 2) (2 x - 1)

Apply the distributive property

3 x \times 2 x + 3 x (- 1) - 2 \times 2 x - 2 (- 1)

Multiply the terms

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Evaluate

3 x \times 2 x

Multiply the numbers

6 x \times x

Multiply the terms

6 x^{2}

6 x^{2} + 3 x (- 1) - 2 \times 2 x - 2 (- 1)

Multiply the terms

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

Multiply the terms

6 x^{2} - 3 x - 4 x - 2 (- 1)

Multiply the terms

6 x^{2} - 3 x - 4 x + 2

6 x^{2} - 3 x - 4 x + 2 - 1

Subtract the terms

More Steps

Evaluate

- 3 x - 4 x

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

(- 3 - 4) x

Subtract the numbers

- 7 x

6 x^{2} - 7 x + 2 - 1

Subtract the numbers

6 x^{2} - 7 x + 1

Rewrite the expression

6 x^{2} + (- 1 - 6) x + 1

Calculate

6 x^{2} - x - 6 x + 1

Rewrite the expression

x \times 6 x - x - 6 x + 1

Factor out x from the expression

x (6 x - 1) - 6 x + 1

Factor out - 1 from the expression

x (6 x - 1) - (6 x - 1)

Solution

(x - 1) (6 x - 1)

Show Solution

Find the roots

x_{1} = \frac{1}{6}, x_{2} = 1

Alternative Form

x_{1} = 0.1 \dot{6}, x_{2} = 1

Evaluate

(3 x - 2) (2 x - 1) - 1

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

(3 x - 2) (2 x - 1) - 1 = 0

Calculate

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Evaluate

(3 x - 2) (2 x - 1) - 1

Expand the expression

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Calculate

(3 x - 2) (2 x - 1)

Apply the distributive property

3 x \times 2 x - 3 x \times 1 - 2 \times 2 x - (- 2 \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

Multiply the numbers

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

Any expression multiplied by 1 remains the same

6 x^{2} - 3 x - 4 x - (- 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

6 x^{2} - 3 x - 4 x + 2

Subtract the terms

6 x^{2} - 7 x + 2

6 x^{2} - 7 x + 2 - 1

Subtract the numbers

6 x^{2} - 7 x + 1

6 x^{2} - 7 x + 1 = 0

Factor the expression

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Evaluate

6 x^{2} - 7 x + 1

Rewrite the expression

6 x^{2} + (- 1 - 6) x + 1

Calculate

6 x^{2} - x - 6 x + 1

Rewrite the expression

x \times 6 x - x - 6 x + 1

Factor out x from the expression

x (6 x - 1) - 6 x + 1

Factor out - 1 from the expression

x (6 x - 1) - (6 x - 1)

Factor out 6 x - 1 from the expression

(x - 1) (6 x - 1)

(x - 1) (6 x - 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 1 = 0 6 x - 1 = 0

Solve the equation for x

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Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 6 x - 1 = 0

Solve the equation for x

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Evaluate

6 x - 1 = 0

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

6 x = 0 + 1

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

6 x = 1

Divide both sides

\frac{6 x}{6} = \frac{1}{6}

Divide the numbers

x = \frac{1}{6}

x = 1 x = \frac{1}{6}

Solution

x_{1} = \frac{1}{6}, x_{2} = 1

Alternative Form

x_{1} = 0.1 \dot{6}, x_{2} = 1

Show Solution