Solve (6x-1)(3x-2)

Question

Simplify the expression

18 x^{2} - 15 x + 2

Evaluate

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

Apply the distributive property

6 x \times 3 x - 6 x \times 2 - 3 x - (- 2)

Multiply the terms

More Steps

Evaluate

6 x \times 3 x

Multiply the numbers

18 x \times x

Multiply the terms

18 x^{2}

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

Multiply the numbers

18 x^{2} - 12 x - 3 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

18 x^{2} - 12 x - 3 x + 2

Solution

More Steps

Evaluate

- 12 x - 3 x

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

(- 12 - 3) x

Subtract the numbers

- 15 x

18 x^{2} - 15 x + 2

Show Solution

Find the roots

x_{1} = \frac{1}{6}, x_{2} = \frac{2}{3}

Alternative Form

x_{1} = 0.1 \dot{6}, x_{2} = 0. \dot{6}

Evaluate

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

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

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

Separate the equation into 2 possible cases

6 x - 1 = 0 3 x - 2 = 0

Solve the equation

More Steps

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 = \frac{1}{6} 3 x - 2 = 0

Solve the equation

More Steps

Evaluate

3 x - 2 = 0

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

3 x = 0 + 2

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

3 x = 2

Divide both sides

\frac{3 x}{3} = \frac{2}{3}

Divide the numbers

x = \frac{2}{3}

x = \frac{1}{6} x = \frac{2}{3}

Solution

x_{1} = \frac{1}{6}, x_{2} = \frac{2}{3}

Alternative Form

x_{1} = 0.1 \dot{6}, x_{2} = 0. \dot{6}

Show Solution