Solve for x
x = \frac{25}{14} = 1\frac{11}{14} \approx 1.785714286
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204+28\left(2x-1\right)-14\left(10x+1\right)=21\left(2x+1\right)-84
Multiply both sides of the equation by 84, the least common multiple of 7,3,6,4.
204+56x-28-14\left(10x+1\right)=21\left(2x+1\right)-84
Use the distributive property to multiply 28 by 2x-1.
176+56x-14\left(10x+1\right)=21\left(2x+1\right)-84
Subtract 28 from 204 to get 176.
176+56x-140x-14=21\left(2x+1\right)-84
Use the distributive property to multiply -14 by 10x+1.
176-84x-14=21\left(2x+1\right)-84
Combine 56x and -140x to get -84x.
162-84x=21\left(2x+1\right)-84
Subtract 14 from 176 to get 162.
162-84x=42x+21-84
Use the distributive property to multiply 21 by 2x+1.
162-84x=42x-63
Subtract 84 from 21 to get -63.
162-84x-42x=-63
Subtract 42x from both sides.
162-126x=-63
Combine -84x and -42x to get -126x.
-126x=-63-162
Subtract 162 from both sides.
-126x=-225
Subtract 162 from -63 to get -225.
x=\frac{-225}{-126}
Divide both sides by -126.
x=\frac{25}{14}
Reduce the fraction \frac{-225}{-126} to lowest terms by extracting and canceling out -9.
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