Solve for x
x = -\frac{341}{19} = -17\frac{18}{19} \approx -17.947368421
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-21\left(x+1\right)+14\left(x+2\right)=6\left(2x-5\right)+378
Multiply both sides of the equation by 42, the least common multiple of 2,3,7.
-21x-21+14\left(x+2\right)=6\left(2x-5\right)+378
Use the distributive property to multiply -21 by x+1.
-21x-21+14x+28=6\left(2x-5\right)+378
Use the distributive property to multiply 14 by x+2.
-7x-21+28=6\left(2x-5\right)+378
Combine -21x and 14x to get -7x.
-7x+7=6\left(2x-5\right)+378
Add -21 and 28 to get 7.
-7x+7=12x-30+378
Use the distributive property to multiply 6 by 2x-5.
-7x+7=12x+348
Add -30 and 378 to get 348.
-7x+7-12x=348
Subtract 12x from both sides.
-19x+7=348
Combine -7x and -12x to get -19x.
-19x=348-7
Subtract 7 from both sides.
-19x=341
Subtract 7 from 348 to get 341.
x=\frac{341}{-19}
Divide both sides by -19.
x=-\frac{341}{19}
Fraction \frac{341}{-19} can be rewritten as -\frac{341}{19} by extracting the negative sign.
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