To solve this equation we need to firast expand it.

x²=4(x-3)²

To do this we first expand the brackets. Remeber anything squared means times it by itself
(x-3)²
=(x-3)(x-3)
=x²-6x+9

This makes the equation look like this
x²=4(x²-6x+9)

We know times the brakcet out by the 4 to give us
x²=4x²-24x+36

To solve this question we need to find x, to this we can see that we can minus x² from both sides
0=3x²-24x+36

we can divide this equation by 3 to give us
0=x²-8x+12

Now to factorise this equation we need to find two numbers that multiply together to make twelve and add together to make -8. This shows us that
0=x²-2x-6x+12
0=x(x-2)-6(x-2)
0=(x-2)(x-6)

Becasue the equation equals 0 we can see that
0=(x-2) 0=(x-6)
0=x-2 0=x-6
x=2 x=6

Thus the solution to x²=4(x-3)² is x=2 or x=6

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