(2mm+2)(4m2+5m-6mn)

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-6=-24 and whose sum is b=5.

Factor 5 out of 5m.

2mm+2⋅4m2+5(m)-6mn

Rewrite 5 as -3 plus 8

2mm+2⋅4m2+(-3+8)m-6mn

Apply the distributive property.

2mm+2⋅4m2-3m+8m-6mn

2mm+2⋅4m2-3m+8m-6mn

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2mm+2⋅(4m2-3m)+8m-6mn

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

2mm+2⋅m(4m-3)+2(4m-3)mn

2mm+2⋅m(4m-3)+2(4m-3)mn

Factor the polynomial by factoring out the greatest common factor, 4m-3.

2mm+2⋅(4m-3)(m+2)mn

2mm+2⋅(4m-3)(m+2)mn

Factor m out of 2m.

m⋅2m+2⋅(4m-3)(m+2)mn

Factor m out of mn.

m⋅2m+2⋅(4m-3)(m+2)m(n)

Cancel the common factor.

m⋅2m+2⋅(4m-3)(m+2)mn

Rewrite the expression.

2m+2⋅(4m-3)(m+2)n

2m+2⋅(4m-3)(m+2)n

Factor m+2 out of (4m-3)(m+2).

2m+2⋅(m+2)(4m-3)n

Cancel the common factor.

2m+2⋅(m+2)(4m-3)n

Rewrite the expression.

24m-3n

24m-3n

Combine 2 and 4m-3n.

2(4m-3)n

Simplify ((2m)/(m+2))((4m^2+5m-6)/(mn))