Solve for x
x=2
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15\left(3x+2\right)-10\left(5x-1\right)=120-6\left(4x+7\right)
Multiply both sides of the equation by 30, the least common multiple of 2,3,5.
45x+30-10\left(5x-1\right)=120-6\left(4x+7\right)
Use the distributive property to multiply 15 by 3x+2.
45x+30-50x+10=120-6\left(4x+7\right)
Use the distributive property to multiply -10 by 5x-1.
-5x+30+10=120-6\left(4x+7\right)
Combine 45x and -50x to get -5x.
-5x+40=120-6\left(4x+7\right)
Add 30 and 10 to get 40.
-5x+40=120-24x-42
Use the distributive property to multiply -6 by 4x+7.
-5x+40=78-24x
Subtract 42 from 120 to get 78.
-5x+40+24x=78
Add 24x to both sides.
19x+40=78
Combine -5x and 24x to get 19x.
19x=78-40
Subtract 40 from both sides.
19x=38
Subtract 40 from 78 to get 38.
x=\frac{38}{19}
Divide both sides by 19.
x=2
Divide 38 by 19 to get 2.
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