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144-24\left(\frac{2a+1}{3}-\frac{1-3a}{4}\right)=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Multiply both sides of the equation by 24, the least common multiple of 3,4,8.
144-24\left(\frac{4\left(2a+1\right)}{12}-\frac{3\left(1-3a\right)}{12}\right)=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{2a+1}{3} times \frac{4}{4}. Multiply \frac{1-3a}{4} times \frac{3}{3}.
144-24\times \frac{4\left(2a+1\right)-3\left(1-3a\right)}{12}=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Since \frac{4\left(2a+1\right)}{12} and \frac{3\left(1-3a\right)}{12} have the same denominator, subtract them by subtracting their numerators.
144-24\times \frac{8a+4-3+9a}{12}=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Do the multiplications in 4\left(2a+1\right)-3\left(1-3a\right).
144-24\times \frac{17a+1}{12}=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Combine like terms in 8a+4-3+9a.
144-2\left(17a+1\right)=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Cancel out 12, the greatest common factor in 24 and 12.
144-34a-2=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Use the distributive property to multiply -2 by 17a+1.
142-34a=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Subtract 2 from 144 to get 142.
142-34a=120-24\left(\frac{3\left(7a-1\right)}{24}-\frac{8\left(5-2a\right)}{24}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 3 is 24. Multiply \frac{7a-1}{8} times \frac{3}{3}. Multiply \frac{5-2a}{3} times \frac{8}{8}.
142-34a=120-24\times \frac{3\left(7a-1\right)-8\left(5-2a\right)}{24}
Since \frac{3\left(7a-1\right)}{24} and \frac{8\left(5-2a\right)}{24} have the same denominator, subtract them by subtracting their numerators.
142-34a=120-24\times \frac{21a-3-40+16a}{24}
Do the multiplications in 3\left(7a-1\right)-8\left(5-2a\right).
142-34a=120-24\times \frac{37a-43}{24}
Combine like terms in 21a-3-40+16a.
142-34a=120-\frac{24\left(37a-43\right)}{24}
Express 24\times \frac{37a-43}{24} as a single fraction.
142-34a=120-\left(37a-43\right)
Cancel out 24 and 24.
142-34a=120-37a-\left(-43\right)
To find the opposite of 37a-43, find the opposite of each term.
142-34a=120-37a+43
The opposite of -43 is 43.
142-34a=163-37a
Add 120 and 43 to get 163.
142-34a+37a=163
Add 37a to both sides.
142+3a=163
Combine -34a and 37a to get 3a.
3a=163-142
Subtract 142 from both sides.
3a=21
Subtract 142 from 163 to get 21.
a=\frac{21}{3}
Divide both sides by 3.
a=7
Divide 21 by 3 to get 7.