Solve 3m^2 =-16m -21

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

m_{1} = - 3, m_{2} = - \frac{7}{3}

Alternative Form

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

Evaluate

3 m^{2} = - 16 m - 21

Move the expression to the left side

3 m^{2} + 16 m + 21 = 0

Factor the expression

More Steps

Evaluate

3 m^{2} + 16 m + 21

Rewrite the expression

3 m^{2} + (7 + 9) m + 21

Calculate

3 m^{2} + 7 m + 9 m + 21

Rewrite the expression

m \times 3 m + m \times 7 + 3 \times 3 m + 3 \times 7

Factor out m from the expression

m (3 m + 7) + 3 \times 3 m + 3 \times 7

Factor out 3 from the expression

m (3 m + 7) + 3 (3 m + 7)

Factor out 3 m + 7 from the expression

(m + 3) (3 m + 7)

(m + 3) (3 m + 7) = 0

When the product of factors equals 0,at least one factor is 0

3 m + 7 = 0 m + 3 = 0

Solve the equation for m

More Steps

Evaluate

3 m + 7 = 0

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

3 m = 0 - 7

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

3 m = - 7

Divide both sides

\frac{3 m}{3} = \frac{- 7}{3}

Divide the numbers

m = \frac{- 7}{3}

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

m = - \frac{7}{3}

m = - \frac{7}{3} m + 3 = 0

Solve the equation for m

More Steps

Evaluate

m + 3 = 0

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

m = 0 - 3

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

m = - 3

m = - \frac{7}{3} m = - 3

Solution

m_{1} = - 3, m_{2} = - \frac{7}{3}

Alternative Form

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

Show Solution