Here are the steps on how to solve the equation:

Expand the left-hand side of the equation.
(3x−2)x+6x1/2=3x2−2x+6x1/2

Simplify the right-hand side of the equation.
(3x−6)(2x+7)=6x2+4x−42

Set the left-hand side and right-hand side equal to each other and solve for x.
3x2−2x+6x1/2=6x2+4x−42

Combine like terms on both sides of the equation.
6x2−2x+6x1/2=6x2+4x−42

Subtract 6x2 from both sides of the equation.
−2x+6x1/2=4x−42

Subtract 4x from both sides of the equation.
6x1/2=−42

Multiply both sides of the equation by 2 to get rid of the fraction.
12x=−84

Divide both sides of the equation by 12 to find x.
x=−7

Therefore, the solution to the equation is x=−7.
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