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5x^{2}=5x^{2}-2\times 5x+12x-24
Multiply both sides of the equation by 6, the least common multiple of 6,3.
5x^{2}=5x^{2}-10x+12x-24
Multiply -2 and 5 to get -10.
5x^{2}=5x^{2}+2x-24
Combine -10x and 12x to get 2x.
5x^{2}-5x^{2}=2x-24
Subtract 5x^{2} from both sides.
0=2x-24
Combine 5x^{2} and -5x^{2} to get 0.
2x-24=0
Swap sides so that all variable terms are on the left hand side.
2x=24
Add 24 to both sides. Anything plus zero gives itself.
x=\frac{24}{2}
Divide both sides by 2.
x=12
Divide 24 by 2 to get 12.