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-45\left(13-x\right)=\left(x-52\right)\times 6
Variable x cannot be equal to 52 since division by zero is not defined. Multiply both sides of the equation by 45\left(x-52\right), the least common multiple of 52-x,45.
-585+45x=\left(x-52\right)\times 6
Use the distributive property to multiply -45 by 13-x.
-585+45x=6x-312
Use the distributive property to multiply x-52 by 6.
-585+45x-6x=-312
Subtract 6x from both sides.
-585+39x=-312
Combine 45x and -6x to get 39x.
39x=-312+585
Add 585 to both sides.
39x=273
Add -312 and 585 to get 273.
x=\frac{273}{39}
Divide both sides by 39.
x=7
Divide 273 by 39 to get 7.