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

**Step 1: Expand the brackets.** (x + 2)(x - 5) = x(x - 5) + 2(x - 5) = x² - 5x + 2x - 10 = x² - 3x - 10 **Step 2: Rearrange the equation into the standard quadratic form ax² + bx + c = 0.** The equation is now: x² - 3x - 10 = 6x Subtract 6x from both sides to make the right side equal to zero: x² - 3x - 6x - 10 = 0 x² - 9x - 10 = 0 **Step 3: Solve the quadratic equation.** We can solve this by factorising or using the quadratic formula. *Method 1: Factorising* We need two numbers that multiply to make -10 and add to make -9. The numbers are -10 and +1. So, we can factorise the equation as: (x - 10)(x + 1) = 0 For the product to be zero, one of the factors must be zero. Either x - 10 = 0 => x = 10 Or x + 1 = 0 => x = -1 *Method 2: Quadratic Formula* For x² - 9x - 10 = 0, we have a=1, b=-9, c=-10. x = [-b ± √(b² - 4ac)] / 2a x = [ -(-9) ± √((-9)² - 4(1)(-10)) ] / (2 * 1) x = [ 9 ± √(81 + 40) ] / 2 x = [ 9 ± √121 ] / 2 x = [ 9 ± 11 ] / 2 So, x = (9 + 11) / 2 = 20 / 2 = 10 Or, x = (9 - 11) / 2 = -2 / 2 = -1 **Answer: x = 10 and x = -1**