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14\left(4x-1\right)-6\left(9x-4\right)-21x+60=7\left(x-5\right)+3\left(2x+3\right)
Multiply both sides of the equation by 42, the least common multiple of 3,7,2,6,14.
56x-14-6\left(9x-4\right)-21x+60=7\left(x-5\right)+3\left(2x+3\right)
Use the distributive property to multiply 14 by 4x-1.
56x-14-54x+24-21x+60=7\left(x-5\right)+3\left(2x+3\right)
Use the distributive property to multiply -6 by 9x-4.
2x-14+24-21x+60=7\left(x-5\right)+3\left(2x+3\right)
Combine 56x and -54x to get 2x.
2x+10-21x+60=7\left(x-5\right)+3\left(2x+3\right)
Add -14 and 24 to get 10.
-19x+10+60=7\left(x-5\right)+3\left(2x+3\right)
Combine 2x and -21x to get -19x.
-19x+70=7\left(x-5\right)+3\left(2x+3\right)
Add 10 and 60 to get 70.
-19x+70=7x-35+3\left(2x+3\right)
Use the distributive property to multiply 7 by x-5.
-19x+70=7x-35+6x+9
Use the distributive property to multiply 3 by 2x+3.
-19x+70=13x-35+9
Combine 7x and 6x to get 13x.
-19x+70=13x-26
Add -35 and 9 to get -26.
-19x+70-13x=-26
Subtract 13x from both sides.
-32x+70=-26
Combine -19x and -13x to get -32x.
-32x=-26-70
Subtract 70 from both sides.
-32x=-96
Subtract 70 from -26 to get -96.
x=\frac{-96}{-32}
Divide both sides by -32.
x=3
Divide -96 by -32 to get 3.