Solve x^2 = 4(x – 3)^2
x2 = 4(x-3)2x2 = 4(x-3)(x-3) - showing that these are double bracketsx2 = 4(x2 - 6x + 9) - expanding the double bracketsx2 = 4x2 - 24x + 36 - multiplying the 4 by the expression inside to remove the brackets0 = 3x2 - 24x + 36 - rearrange to make the equation equal to 00 = x2 - 8x + 12 - realise that there is a common factor of 3 so divide by 3 to simplify the equation0 = (x-6)(x-2) - factorise the expression by finding two numbers that add to (-8) and multiply to make (+12).Finally solve each bracket separately by making them equal to 0 and rearranging for x. x - 6 = 0 so x = 6or x - 2 = 0 so x = 2
