Final answer:
To solve the equation (6 - 2x)(3 - 2x)X = 40, we need to expand the brackets, simplify to a cubic equation, and then solve for x. Generally, we would use factoring or the quadratic formula, but with a cubic term present, more advanced methods may be required.
Step-by-step explanation:
The equation in question is (6 - 2x)(3 - 2x)X = 40, and we need to solve it for real values of x. This is a quadratic equation once expanded and simplified.
First, we expand the equation:
- Expand (6 - 2x)(3 - 2x) to get 18 - 12x + 4x²
- Multiply the entire expression by X to get 18X - 12xX + 4x³
- Set it equal to 40 to form the equation: 4x³ - 12xX + 18X = 40
Next, subtract 40 from both sides to get a quadratic equation in standard form:
- 4x³ - 12xX + 18X - 40 = 0
To solve for x, we might try factoring if possible, or use the quadratic formula. However, this equation has a cubic term, which implies we need methods beyond simple quadratic techniques. Without a proper expansion and simplification, it's tough to provide a solution based only on the information given. We might need numerical methods or further information on how to handle the cubic term.