Solve for x
x=-15
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1665\left(x+2\right)+1443\left(2x+45\right)=585\left(3x+8\right)+2405\left(4x+69\right)
Multiply both sides of the equation by 21645, the least common multiple of 13,15,37,9.
1665x+3330+1443\left(2x+45\right)=585\left(3x+8\right)+2405\left(4x+69\right)
Use the distributive property to multiply 1665 by x+2.
1665x+3330+2886x+64935=585\left(3x+8\right)+2405\left(4x+69\right)
Use the distributive property to multiply 1443 by 2x+45.
4551x+3330+64935=585\left(3x+8\right)+2405\left(4x+69\right)
Combine 1665x and 2886x to get 4551x.
4551x+68265=585\left(3x+8\right)+2405\left(4x+69\right)
Add 3330 and 64935 to get 68265.
4551x+68265=1755x+4680+2405\left(4x+69\right)
Use the distributive property to multiply 585 by 3x+8.
4551x+68265=1755x+4680+9620x+165945
Use the distributive property to multiply 2405 by 4x+69.
4551x+68265=11375x+4680+165945
Combine 1755x and 9620x to get 11375x.
4551x+68265=11375x+170625
Add 4680 and 165945 to get 170625.
4551x+68265-11375x=170625
Subtract 11375x from both sides.
-6824x+68265=170625
Combine 4551x and -11375x to get -6824x.
-6824x=170625-68265
Subtract 68265 from both sides.
-6824x=102360
Subtract 68265 from 170625 to get 102360.
x=\frac{102360}{-6824}
Divide both sides by -6824.
x=-15
Divide 102360 by -6824 to get -15.
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