Solve (x + 2)(x - 5) = 6x

The given equation is (x + 2)(x - 5) = 6x. **1. Expand the brackets:** We use the FOIL method (First, Outer, Inner, Last): (x * x) + (x * -5) + (2 * x) + (2 * -5) = x² - 5x + 2x - 10 Combine the x terms: = x² - 3x - 10 So the equation is now: x² - 3x - 10 = 6x **2. Rearrange to standard quadratic form (ax² + bx + c = 0):** Subtract 6x from both sides: x² - 3x - 6x - 10 = 0 x² - 9x - 10 = 0 **3. Solve the quadratic equation:** We can factorise this expression. We are looking for two numbers that multiply to give -10 and add to give -9. These numbers are -10 and +1. So, the equation becomes: (x - 10)(x + 1) = 0 This gives two possible solutions: - If x - 10 = 0, then x = 10. - If x + 1 = 0, then x = -1. The solutions are x = 10 and x = -1.