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2\times 2x+32=-3\times 4x
Multiply both sides of the equation by 6, the least common multiple of 3,2.
4x+32=-3\times 4x
Multiply 2 and 2 to get 4.
4x+32=-12x
Multiply -3 and 4 to get -12.
4x+32+12x=0
Add 12x to both sides.
16x+32=0
Combine 4x and 12x to get 16x.
16x=-32
Subtract 32 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-32}{16}
Divide both sides by 16.
x=-2
Divide -32 by 16 to get -2.