Solve (3x-10)*(2x-3)

Question

Simplify the expression

6 x^{2} - 29 x + 30

Evaluate

(3 x - 10) (2 x - 3)

Apply the distributive property

3 x \times 2 x - 3 x \times 3 - 10 \times 2 x - (- 10 \times 3)

Multiply the terms

More Steps

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 3 - 10 \times 2 x - (- 10 \times 3)

Multiply the numbers

6 x^{2} - 9 x - 10 \times 2 x - (- 10 \times 3)

Multiply the numbers

6 x^{2} - 9 x - 20 x - (- 10 \times 3)

Multiply the numbers

6 x^{2} - 9 x - 20 x - (- 30)

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} - 9 x - 20 x + 30

Solution

More Steps

Evaluate

- 9 x - 20 x

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

(- 9 - 20) x

Subtract the numbers

- 29 x

6 x^{2} - 29 x + 30

Show Solution

Find the roots

x_{1} = \frac{3}{2}, x_{2} = \frac{10}{3}

Alternative Form

x_{1} = 1.5, x_{2} = 3. \dot{3}

Evaluate

(3 x - 10) (2 x - 3)

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

(3 x - 10) (2 x - 3) = 0

Separate the equation into 2 possible cases

3 x - 10 = 0 2 x - 3 = 0

Solve the equation

More Steps

Evaluate

3 x - 10 = 0

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

3 x = 0 + 10

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

3 x = 10

Divide both sides

\frac{3 x}{3} = \frac{10}{3}

Divide the numbers

x = \frac{10}{3}

x = \frac{10}{3} 2 x - 3 = 0

Solve the equation

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{2}

x = \frac{10}{3} x = \frac{3}{2}

Solution

x_{1} = \frac{3}{2}, x_{2} = \frac{10}{3}

Alternative Form

x_{1} = 1.5, x_{2} = 3. \dot{3}

Show Solution