x^2 = 4(x – 3)^2

This is a quadratic equation, which contains terms up to x². All quadratic equations can be written in the form ax² + bx + c = 0 where a, b and c are numbers, and a cannot be equal to zero. Expand the brackets: x² = 4(x² - 6x + 9). Multiply RHS brackets by 4: x² = 4x² - 24x + 36. Collect x's on one side: 3x² - 24x + 36 = 0. Simplify: x² - 8x + 12 = 0. Factorise: (x - 6)(x - 2) = 0. The product of x - 6 and x - 2 is 0, so one or both brackets must also be equal to 0, hence x = 6 or x = 2. Alternatively you can use the quadratic formula provided in the formula sheet and substitute the corresponding numbers in, or solve by completing the square.