Solve (-7m-9) (-6m-5)

Question

Simplify the expression

42 m^{2} + 89 m + 45

Evaluate

(- 7 m - 9) (- 6 m - 5)

Apply the distributive property

- 7 m (- 6 m) - (- 7 m \times 5) - 9 (- 6 m) - (- 9 \times 5)

Multiply the terms

More Steps

Evaluate

- 7 m (- 6 m)

Multiply the numbers

More Steps

Evaluate

- 7 (- 6)

Multiplying or dividing an even number of negative terms equals a positive

7 \times 6

Multiply the numbers

42

42 m \times m

Multiply the terms

42 m^{2}

42 m^{2} - (- 7 m \times 5) - 9 (- 6 m) - (- 9 \times 5)

Multiply the numbers

42 m^{2} - (- 35 m) - 9 (- 6 m) - (- 9 \times 5)

Multiply the numbers

More Steps

Evaluate

- 9 (- 6)

Multiplying or dividing an even number of negative terms equals a positive

9 \times 6

Multiply the numbers

54

42 m^{2} - (- 35 m) + 54 m - (- 9 \times 5)

Multiply the numbers

42 m^{2} - (- 35 m) + 54 m - (- 45)

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

42 m^{2} + 35 m + 54 m + 45

Solution

More Steps

Evaluate

35 m + 54 m

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

(35 + 54) m

Add the numbers

89 m

42 m^{2} + 89 m + 45

Show Solution

Find the roots

m_{1} = - \frac{9}{7}, m_{2} = - \frac{5}{6}

Alternative Form

m_{1} = - 1. \dot{2} 8571 \dot{4}, m_{2} = - 0.8 \dot{3}

Evaluate

(- 7 m - 9) (- 6 m - 5)

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

(- 7 m - 9) (- 6 m - 5) = 0

Change the sign

(7 m + 9) (- 6 m - 5) = 0

Separate the equation into 2 possible cases

7 m + 9 = 0 - 6 m - 5 = 0

Solve the equation

More Steps

Evaluate

7 m + 9 = 0

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

7 m = 0 - 9

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

7 m = - 9

Divide both sides

\frac{7 m}{7} = \frac{- 9}{7}

Divide the numbers

m = \frac{- 9}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

m = - \frac{9}{7}

m = - \frac{9}{7} - 6 m - 5 = 0

Solve the equation

More Steps

Evaluate

- 6 m - 5 = 0

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

- 6 m = 0 + 5

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

- 6 m = 5

Change the signs on both sides of the equation

6 m = - 5

Divide both sides

\frac{6 m}{6} = \frac{- 5}{6}

Divide the numbers

m = \frac{- 5}{6}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

m = - \frac{5}{6}

m = - \frac{9}{7} m = - \frac{5}{6}

Solution

m_{1} = - \frac{9}{7}, m_{2} = - \frac{5}{6}

Alternative Form

m_{1} = - 1. \dot{2} 8571 \dot{4}, m_{2} = - 0.8 \dot{3}

Show Solution