Solve for x
x=6
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\left(x-7\right)\times 6=\left(x-5\right)\left(-6\right)
Variable x cannot be equal to any of the values 5,7 since division by zero is not defined. Multiply both sides of the equation by \left(x-7\right)\left(x-5\right), the least common multiple of x-5,x-7.
6x-42=\left(x-5\right)\left(-6\right)
Use the distributive property to multiply x-7 by 6.
6x-42=-6x+30
Use the distributive property to multiply x-5 by -6.
6x-42+6x=30
Add 6x to both sides.
12x-42=30
Combine 6x and 6x to get 12x.
12x=30+42
Add 42 to both sides.
12x=72
Add 30 and 42 to get 72.
x=\frac{72}{12}
Divide both sides by 12.
x=6
Divide 72 by 12 to get 6.
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