Solve (6f-7)(8f-9)

Question

Simplify the expression

48 f^{2} - 110 f + 63

Evaluate

(6 f - 7) (8 f - 9)

Apply the distributive property

6 f \times 8 f - 6 f \times 9 - 7 \times 8 f - (- 7 \times 9)

Multiply the terms

More Steps

Evaluate

6 f \times 8 f

Multiply the numbers

48 f \times f

Multiply the terms

48 f^{2}

48 f^{2} - 6 f \times 9 - 7 \times 8 f - (- 7 \times 9)

Multiply the numbers

48 f^{2} - 54 f - 7 \times 8 f - (- 7 \times 9)

Multiply the numbers

48 f^{2} - 54 f - 56 f - (- 7 \times 9)

Multiply the numbers

48 f^{2} - 54 f - 56 f - (- 63)

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

48 f^{2} - 54 f - 56 f + 63

Solution

More Steps

Evaluate

- 54 f - 56 f

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

(- 54 - 56) f

Subtract the numbers

- 110 f

48 f^{2} - 110 f + 63

Show Solution

Find the roots

f_{1} = \frac{9}{8}, f_{2} = \frac{7}{6}

Alternative Form

f_{1} = 1.125, f_{2} = 1.1 \dot{6}

Evaluate

(6 f - 7) (8 f - 9)

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

(6 f - 7) (8 f - 9) = 0

Separate the equation into 2 possible cases

6 f - 7 = 0 8 f - 9 = 0

Solve the equation

More Steps

Evaluate

6 f - 7 = 0

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

6 f = 0 + 7

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

6 f = 7

Divide both sides

\frac{6 f}{6} = \frac{7}{6}

Divide the numbers

f = \frac{7}{6}

f = \frac{7}{6} 8 f - 9 = 0

Solve the equation

More Steps

Evaluate

8 f - 9 = 0

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

8 f = 0 + 9

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

8 f = 9

Divide both sides

\frac{8 f}{8} = \frac{9}{8}

Divide the numbers

f = \frac{9}{8}

f = \frac{7}{6} f = \frac{9}{8}

Solution

f_{1} = \frac{9}{8}, f_{2} = \frac{7}{6}

Alternative Form

f_{1} = 1.125, f_{2} = 1.1 \dot{6}

Show Solution