factor 16d^2-28d-30 — step-by-step solution

Let's factorize in

ℝ

16 d^{2} - 28 d - 30

You can write the expression in factored form:

2 \cdot (8 d^{2} - 14 d - 15)

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-14)}^{2} - 4 \cdot 8 \cdot (-15)

ℹ

{(-14)}^{2}

196

‖

4 \cdot 8

32

Δ = 196 + 32 \cdot 15

Δ = 196 + 480

Δ = 676

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

d1 = \frac{14 - \sqrt{676}}{2 \cdot 8}

ℹ

- \sqrt{676}

-26

‖

2 \cdot 8

16

d1 = \frac{14 - 26}{16}

d1 = - \frac{12}{16}

d1 = - \frac{3}{4}

Solution second:

\frac{- b + \sqrt{Δ}}{2 a}

d2 = \frac{14 + \sqrt{676}}{2 \cdot 8}

ℹ

\sqrt{676}

26

‖

2 \cdot 8

16

d2 = \frac{14 + 26}{16}

d2 = \frac{40}{16}

d2 = \frac{5}{2}

Factors found:

8 \cdot (d + \frac{3}{4}) \cdot (d - \frac{5}{2})

2 \cdot 8 \cdot (d + \frac{3}{4}) \cdot (d - \frac{5}{2})

▶Factored expression:

16 \cdot (d + \frac{3}{4}) \cdot (d - \frac{5}{2})