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

Start by look at the right hand side of the equation, first expand (x-3)² which is also the same as (x-3)(x-3). This comes out to equal (x²-6x+9). Next multiply (x² -6x+9) by 4 which was left outside of the bracket before it was expanded. This comes out to equal (4x²-24x+36).Now you are left with (x²=4x²-24x+36), minus the (x²) from the left hand side (to group all of the x values onto one side of the equation) to get (0=3x²-24x+36), divide through by 3 (due to 3 being a common factor through the equation) to simplify the equation. Next factorise the quadratic equation, which comes to being (x-2)(x-6)=0. Therefore the solutions of the equations are x=2 and x=6. To prove the solutions are correct, substitute each of the values separately and for the solution to be correct it should end up 0=0.