Simplify (z^2-3z-18)/(7z^3-4z^2)*(x(49z^3-16z))/(6z-36)

Math
z2-3z-187z3-4z2⋅x(49z3-16z)6z-36
Factor z2-3z-18 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -18 and whose sum is -3.
-6,3
Write the factored form using these integers.
(z-6)(z+3)7z3-4z2⋅x(49z3-16z)6z-36
(z-6)(z+3)7z3-4z2⋅x(49z3-16z)6z-36
Factor z2 out of 7z3-4z2.
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Factor z2 out of 7z3.
(z-6)(z+3)z2(7z)-4z2⋅x(49z3-16z)6z-36
Factor z2 out of -4z2.
(z-6)(z+3)z2(7z)+z2⋅-4⋅x(49z3-16z)6z-36
Factor z2 out of z2(7z)+z2⋅-4.
(z-6)(z+3)z2(7z-4)⋅x(49z3-16z)6z-36
(z-6)(z+3)z2(7z-4)⋅x(49z3-16z)6z-36
Simplify the numerator.
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Factor z out of 49z3-16z.
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Factor z out of 49z3.
(z-6)(z+3)z2(7z-4)⋅x(z(49z2)-16z)6z-36
Factor z out of -16z.
(z-6)(z+3)z2(7z-4)⋅x(z(49z2)+z⋅-16)6z-36
Factor z out of z(49z2)+z⋅-16.
(z-6)(z+3)z2(7z-4)⋅x(z(49z2-16))6z-36
(z-6)(z+3)z2(7z-4)⋅x(z(49z2-16))6z-36
Rewrite 49z2 as (7z)2.
(z-6)(z+3)z2(7z-4)⋅x(z((7z)2-16))6z-36
Rewrite 16 as 42.
(z-6)(z+3)z2(7z-4)⋅x(z((7z)2-42))6z-36
Factor.
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)6z-36
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)6z-36
Simplify terms.
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Factor 6 out of 6z-36.
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Factor 6 out of 6z.
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)6(z)-36
Factor 6 out of -36.
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)6z+6⋅-6
Factor 6 out of 6z+6⋅-6.
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)6(z-6)
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)6(z-6)
Cancel the common factor of z-6.
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Factor z-6 out of 6(z-6).
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)(z-6)⋅6
Cancel the common factor.
(z-6)(z+3)z2(7z-4)⋅xz(7z+4)(7z-4)(z-6)⋅6
Rewrite the expression.
z+3z2(7z-4)⋅xz(7z+4)(7z-4)6
z+3z2(7z-4)⋅xz(7z+4)(7z-4)6
Cancel the common factor of (z)(7z-4).
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Factor (z)(7z-4) out of z2(7z-4).
z+3z(7z-4)(z)⋅xz(7z+4)(7z-4)6
Factor (z)(7z-4) out of xz(7z+4)(7z-4).
z+3z(7z-4)(z)⋅z(7z-4)(x(7z+4))6
Cancel the common factor.
z+3z(7z-4)z⋅z(7z-4)(x(7z+4))6
Rewrite the expression.
z+3z⋅x(7z+4)6
z+3z⋅x(7z+4)6
Multiply z+3z and x(7z+4)6.
(z+3)(x(7z+4))z⋅6
Simplify the expression.
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Move 6 to the left of z.
(z+3)x(7z+4)6⋅z
Reorder factors in (z+3)x(7z+4)6z.
x(z+3)(7z+4)6z
x(z+3)(7z+4)6z
x(z+3)(7z+4)6z
Simplify (z^2-3z-18)/(7z^3-4z^2)*(x(49z^3-16z))/(6z-36)

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