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15\times 5=x\left(7\times 15+1\right)
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15x, the least common multiple of x,15.
75=x\left(7\times 15+1\right)
Multiply 15 and 5 to get 75.
75=x\left(105+1\right)
Multiply 7 and 15 to get 105.
75=x\times 106
Add 105 and 1 to get 106.
x\times 106=75
Swap sides so that all variable terms are on the left hand side.
x=\frac{75}{106}
Divide both sides by 106.