Solve (3x-8) (2x-5)

Question

Simplify the expression

6 x^{2} - 31 x + 40

Evaluate

(3 x - 8) (2 x - 5)

Apply the distributive property

3 x \times 2 x - 3 x \times 5 - 8 \times 2 x - (- 8 \times 5)

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 5 - 8 \times 2 x - (- 8 \times 5)

Multiply the numbers

6 x^{2} - 15 x - 8 \times 2 x - (- 8 \times 5)

Multiply the numbers

6 x^{2} - 15 x - 16 x - (- 8 \times 5)

Multiply the numbers

6 x^{2} - 15 x - 16 x - (- 40)

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} - 15 x - 16 x + 40

Solution

More Steps

Evaluate

- 15 x - 16 x

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

(- 15 - 16) x

Subtract the numbers

- 31 x

6 x^{2} - 31 x + 40

Show Solution

Find the roots

x_{1} = \frac{5}{2}, x_{2} = \frac{8}{3}

Alternative Form

x_{1} = 2.5, x_{2} = 2. \dot{6}

Evaluate

(3 x - 8) (2 x - 5)

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

(3 x - 8) (2 x - 5) = 0

Separate the equation into 2 possible cases

3 x - 8 = 0 2 x - 5 = 0

Solve the equation

More Steps

Evaluate

3 x - 8 = 0

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

3 x = 0 + 8

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

3 x = 8

Divide both sides

\frac{3 x}{3} = \frac{8}{3}

Divide the numbers

x = \frac{8}{3}

x = \frac{8}{3} 2 x - 5 = 0

Solve the equation

More Steps

Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

\frac{2 x}{2} = \frac{5}{2}

Divide the numbers

x = \frac{5}{2}

x = \frac{8}{3} x = \frac{5}{2}

Solution

x_{1} = \frac{5}{2}, x_{2} = \frac{8}{3}

Alternative Form

x_{1} = 2.5, x_{2} = 2. \dot{6}

Show Solution