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x\times 5+\left(x+3\right)\times 2=0
Variable x cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+3\right), the least common multiple of x+3,x.
x\times 5+2x+6=0
Use the distributive property to multiply x+3 by 2.
7x+6=0
Combine x\times 5 and 2x to get 7x.
7x=-6
Subtract 6 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-6}{7}
Divide both sides by 7.
x=-\frac{6}{7}
Fraction \frac{-6}{7} can be rewritten as -\frac{6}{7} by extracting the negative sign.