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

Math
4x(x-3)-5(3-x)
Apply the distributive property.
4x⋅x+4x⋅-3-5(3-x)
Multiply x by x by adding the exponents.
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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
Factor by grouping.
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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.
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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.
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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)

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