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8x+12=0
Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}. Anything times zero gives zero.
8x=-12
Subtract 12 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-12}{8}
Divide both sides by 8.
x=-\frac{3}{2}
Reduce the fraction \frac{-12}{8} to lowest terms by extracting and canceling out 4.