Solve 5x^(2)+13x+6

Question

Factor the expression

(x + 2) (5 x + 3)

Evaluate

5 x^{2} + 13 x + 6

Rewrite the expression

5 x^{2} + (3 + 10) x + 6

Calculate

5 x^{2} + 3 x + 10 x + 6

Rewrite the expression

x \times 5 x + x \times 3 + 2 \times 5 x + 2 \times 3

Factor out x from the expression

x (5 x + 3) + 2 \times 5 x + 2 \times 3

Factor out 2 from the expression

x (5 x + 3) + 2 (5 x + 3)

Solution

(x + 2) (5 x + 3)

Show Solution

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

Alternative Form

x_{1} = - 2, x_{2} = - 0.6

Evaluate

5 x^{2} + 13 x + 6

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

5 x^{2} + 13 x + 6 = 0

Factor the expression

More Steps

Evaluate

5 x^{2} + 13 x + 6

Rewrite the expression

5 x^{2} + (3 + 10) x + 6

Calculate

5 x^{2} + 3 x + 10 x + 6

Rewrite the expression

x \times 5 x + x \times 3 + 2 \times 5 x + 2 \times 3

Factor out x from the expression

x (5 x + 3) + 2 \times 5 x + 2 \times 3

Factor out 2 from the expression

x (5 x + 3) + 2 (5 x + 3)

Factor out 5 x + 3 from the expression

(x + 2) (5 x + 3)

(x + 2) (5 x + 3) = 0

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

x + 2 = 0 5 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = - 2 5 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 3 = 0

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

5 x = 0 - 3

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

5 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{5}

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

x = - \frac{3}{5}

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

Solution

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

Alternative Form

x_{1} = - 2, x_{2} = - 0.6

Show Solution