factor 6t^2+13t+6 — step-by-step solution

⚠Ⓘ 6t is read as the product 6*t: for a power, write 6^t‖13t is read as the product 13*t: for a power, write 13^t

Let's factor in

ℝ

6 t^{2} + 13 t + 6

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 13^{2} - 4 \cdot 6 \cdot 6

ℹ

13^{2}

169

‖

4 \cdot 6

24

Δ = 169 - 24 \cdot 6

Δ = 169 - 144

Δ = 25

Since

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

t1 = \frac{- 13 - \sqrt{25}}{2 \cdot 6}

ℹ

- \sqrt{25}

-5

‖

2 \cdot 6

12

t1 = \frac{- 13 - 5}{12}

t1 = - \frac{18}{12}

t1 = - \frac{3}{2}

For the second solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

t2 = \frac{- 13 + \sqrt{25}}{2 \cdot 6}

ℹ

\sqrt{25}

5

‖

2 \cdot 6

12

t2 = \frac{- 13 + 5}{12}

t2 = - \frac{8}{12}

t2 = - \frac{2}{3}

▶Factors identified:

6 \cdot (t + \frac{2}{3}) \cdot (t + \frac{3}{2})