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

First multiply out the bracket.x^2 = 4(x - 3)^2 then becomes x^2 = 4(x^2 - 6x + 9)Expand the right hand side further. x^2 = 4x^2 - 24x + 36Collect like terms. 3x^2 - 24x + 36 = 0The number 3 is a common factor of each coefficient. Divide through by 3.x^2 - 8x + 12 = 0Factorise the equation by looking for two numbers that multiply to create 12 and add to create -8. Consider the factorisation of 12 to find these numbers.Common Factors of 12: (1,12), (2,6), (3,4), (-1,-12), (-2,-6), (-3,-4)-2 x -6 = 12 and -2 + -6 = -8Therefore the equation can be factorised:(x - 2)(x - 6) = 0Either (x - 2) or (x - 6) must be equal to zero. Solve for x by setting each one equal to 0.Therefore, x = 2, 6.