(5x+6)÷25×2-365×2+29x-42

To divide by a fraction, multiply by its reciprocal.

(5x+6)5×2+29x-4225×2-36

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅-42=-210 and whose sum is b=29.

Factor 29 out of 29x.

(5x+6)5×2+29(x)-4225×2-36

Rewrite 29 as -6 plus 35

(5x+6)5×2+(-6+35)x-4225×2-36

Apply the distributive property.

(5x+6)5×2-6x+35x-4225×2-36

(5x+6)5×2-6x+35x-4225×2-36

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5x+6)(5×2-6x)+35x-4225×2-36

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

(5x+6)x(5x-6)+7(5x-6)25×2-36

(5x+6)x(5x-6)+7(5x-6)25×2-36

Factor the polynomial by factoring out the greatest common factor, 5x-6.

(5x+6)(5x-6)(x+7)25×2-36

(5x+6)(5x-6)(x+7)25×2-36

Rewrite 25×2 as (5x)2.

(5x+6)(5x-6)(x+7)(5x)2-36

Rewrite 36 as 62.

(5x+6)(5x-6)(x+7)(5x)2-62

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=5x and b=6.

(5x+6)(5x-6)(x+7)(5x+6)(5x-6)

(5x+6)(5x-6)(x+7)(5x+6)(5x-6)

Cancel the common factor of 5x+6.

Cancel the common factor.

(5x+6)(5x-6)(x+7)(5x+6)(5x-6)

Rewrite the expression.

(5x-6)(x+7)5x-6

(5x-6)(x+7)5x-6

Cancel the common factor of 5x-6.

Cancel the common factor.

(5x-6)(x+7)5x-6

Divide x+7 by 1.

x+7

x+7

x+7

Simplify (5x+6)÷((25x^2-36)/(5x^2+29x-42))