Solve x^2 = 4(x-3)^2

First expand the bracket (x-3)² separately to give x² - 6x +9 Next multiply by the 4 outside the brackets to give 4x² -24x +36 Now all the terms have been expanded you can collect the like terms in the equation x² = 4x² -24x +36 Bring the x² to the right side of the equation to give 0 = 3x² -24x +36 Divide this equation by 3, 0 = x² -8x +12 (1) Factorise (1) by finding a pair of numbers that add to -8 and multiply to make 12. Both numbers need to be negative. -6 and -2 are the correct numbers. Therefore (x-2)(x-6) = 0 For this solution to equal 0 overall x must be equal to 2 or 6