2d2+7d-45d2+20d

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-4=-8 and whose sum is b=7.

Factor 7 out of 7d.

2d2+7(d)-45d2+20d

Rewrite 7 as -1 plus 8

2d2+(-1+8)d-45d2+20d

Apply the distributive property.

2d2-1d+8d-45d2+20d

2d2-1d+8d-45d2+20d

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2d2-1d)+8d-45d2+20d

Factor out the greatest common factor (GCF) from each group.

d(2d-1)+4(2d-1)5d2+20d

d(2d-1)+4(2d-1)5d2+20d

Factor the polynomial by factoring out the greatest common factor, 2d-1.

(2d-1)(d+4)5d2+20d

(2d-1)(d+4)5d2+20d

Factor 5d out of 5d2.

(2d-1)(d+4)5d(d)+20d

Factor 5d out of 20d.

(2d-1)(d+4)5d(d)+5d(4)

Factor 5d out of 5d(d)+5d(4).

(2d-1)(d+4)5d(d+4)

(2d-1)(d+4)5d(d+4)

Cancel the common factor.

(2d-1)(d+4)5d(d+4)

Rewrite the expression.

2d-15d

2d-15d

Simplify (2d^2+7d-4)/(5d^2+20d)