2x(x-7)=3x-21 ..............

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To solve this equation, we can follow these steps:

Distribute the 2x on the left side of the equation
2x x - 2x 7 = 3x - 2
2x^2 - 14x = 3x - 21

Move all terms to one side of the equation by subtracting 3x from both sides
2x^2 - 14x - 3x = -2
2x^2 - 17x = -21

Set the equation equal to 0
2x^2 - 17x + 21 = 0

Factor the quadratic equation
We can factor 2x^2 - 17x + 21 by finding two numbers that multiply to 42 (2*21) and add to -17. The numbers are -14 and -3
(2x - 3)(x - 7) = 0

Set each factor to 0 and solve for x
2x - 3 =
2x =
x = 3/2

and

x - 7 =
x = 7

Therefore, the solutions to the equation are x = 3/2 and x = 7.