x(x-6)=4(x+6)
Multiply out:
x² - 6x = 4x + 24
x² - 6x - 4x - 24 = 0
x² - 10x - 24 = 0
This is a quadratic equation
x² - 10x - 24 = 0 Divide through by 2
Multiply first and last coefficients: 1*-24 = -24
We look for two numbers that multiply to give -24, and add to give -10
Those two numbers are -12 and 2.
Check: -12*2 = -24 2 + -12 = -10
We replace the middle term of -10x in the quadratic expression with 2x -12x
x² - 10x - 24 = 0
x² + 2x - 12x - 24 = 0
x(x + 2) - 12(x + 2) = 0
(x + 2)(x - 12) = 0
x + 2 = 0 or x - 12 = 0
x = 0 -2 x = 0 + 12
x = -2 x = 12
The solutions are x = -2 or 12