4x(x-3)-5(3-x)

Apply the distributive property.

4x⋅x+4x⋅-3-5(3-x)

Move x.

4(x⋅x)+4x⋅-3-5(3-x)

Multiply x by x.

4×2+4x⋅-3-5(3-x)

4×2+4x⋅-3-5(3-x)

Multiply -3 by 4.

4×2-12x-5(3-x)

Apply the distributive property.

4×2-12x-5⋅3-5(-x)

Multiply -5 by 3.

4×2-12x-15-5(-x)

Multiply -1 by -5.

4×2-12x-15+5x

Add -12x and 5x.

4×2-7x-15

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⋅-15=-60 and whose sum is b=-7.

Factor -7 out of -7x.

4×2-7(x)-15

Rewrite -7 as 5 plus -12

4×2+(5-12)x-15

Apply the distributive property.

4×2+5x-12x-15

4×2+5x-12x-15

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4×2+5x)-12x-15

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

x(4x+5)-3(4x+5)

x(4x+5)-3(4x+5)

Factor the polynomial by factoring out the greatest common factor, 4x+5.

(4x+5)(x-3)

(4x+5)(x-3)

Factor 4x(x-3)-5(3-x)