Final answer:
The equation ((2x-1)(3x) div (3)(4)=(5)(6)) simplifies to ((1/2)x^2 - (1/4)x) = 30. Solve by forming a quadratic equation and using the quadratic formula or factoring.
Step-by-step explanation:
To solve the given equation ((2x−1)(3x) div (3)(4)=(5)(6)), first, we simplify the expression by multiplying the terms in the numerator and then dividing by the terms in the denominator. We perform the multiplication in the numerator (3x times 2x gives 6x² and 3x times −1 gives −3x), which results in 6x^2 −3x. After simplifying the denominator by multiplying 3 and 4, we get 12. Applying it to the equation, we have (6x²−3x)/12 = 5*6.
Next, we can simplify the left side by dividing each term by 12, which gives (1/2)x^2 − (1/4)x. Now we have the equation (1/2)x^2 − (1/4)x = 30. The last step is to solve for x. We move all terms to one side to form a quadratic equation and then use the quadratic formula or factoring, depending on the situation, to find the value of x.