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\left(2x+5\right)\times 4-\left(x-3\right)\times 8+\left(2x+5\right)\times 3=0
Variable x cannot be equal to any of the values -\frac{5}{2},3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(2x+5\right), the least common multiple of x-3,2x+5.
8x+20-\left(x-3\right)\times 8+\left(2x+5\right)\times 3=0
Use the distributive property to multiply 2x+5 by 4.
8x+20-\left(8x-24\right)+\left(2x+5\right)\times 3=0
Use the distributive property to multiply x-3 by 8.
8x+20-8x+24+\left(2x+5\right)\times 3=0
To find the opposite of 8x-24, find the opposite of each term.
20+24+\left(2x+5\right)\times 3=0
Combine 8x and -8x to get 0.
44+\left(2x+5\right)\times 3=0
Add 20 and 24 to get 44.
44+6x+15=0
Use the distributive property to multiply 2x+5 by 3.
59+6x=0
Add 44 and 15 to get 59.
6x=-59
Subtract 59 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-59}{6}
Divide both sides by 6.
x=-\frac{59}{6}
Fraction \frac{-59}{6} can be rewritten as -\frac{59}{6} by extracting the negative sign.