Solve 3x^2 +19x+20

Question

Factor the expression

(x + 5) (3 x + 4)

Evaluate

3 x^{2} + 19 x + 20

Rewrite the expression

3 x^{2} + (4 + 15) x + 20

Calculate

3 x^{2} + 4 x + 15 x + 20

Rewrite the expression

x \times 3 x + x \times 4 + 5 \times 3 x + 5 \times 4

Factor out x from the expression

x (3 x + 4) + 5 \times 3 x + 5 \times 4

Factor out 5 from the expression

x (3 x + 4) + 5 (3 x + 4)

Solution

(x + 5) (3 x + 4)

Show Solution

x_{1} = - 5, x_{2} = - \frac{4}{3}

Alternative Form

x_{1} = - 5, x_{2} = - 1. \dot{3}

Evaluate

3 x^{2} + 19 x + 20

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

3 x^{2} + 19 x + 20 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 19 x + 20

Rewrite the expression

3 x^{2} + (4 + 15) x + 20

Calculate

3 x^{2} + 4 x + 15 x + 20

Rewrite the expression

x \times 3 x + x \times 4 + 5 \times 3 x + 5 \times 4

Factor out x from the expression

x (3 x + 4) + 5 \times 3 x + 5 \times 4

Factor out 5 from the expression

x (3 x + 4) + 5 (3 x + 4)

Factor out 3 x + 4 from the expression

(x + 5) (3 x + 4)

(x + 5) (3 x + 4) = 0

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

x + 5 = 0 3 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

x + 5 = 0

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

x = 0 - 5

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

x = - 5

x = - 5 3 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 4 = 0

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

3 x = 0 - 4

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

3 x = - 4

Divide both sides

\frac{3 x}{3} = \frac{- 4}{3}

Divide the numbers

x = \frac{- 4}{3}

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

x = - \frac{4}{3}

x = - 5 x = - \frac{4}{3}

Solution

x_{1} = - 5, x_{2} = - \frac{4}{3}

Alternative Form

x_{1} = - 5, x_{2} = - 1. \dot{3}

Show Solution