Question

What are the values of x in the equation x(x+6)=4(x+6)

Answer 1

x(x + 6) = 4(x + 6)
x(x) + x(6) = 4(x) + 4(6)
x² + 6x = 4x + 24
 - 4x - 4x
x² + 2x = 24
x² + 2x - 24 = 24 - 24
x² + 2x - 24 = 0
x = -(2) ± √((2)² - 4(1)(-24))
2(1)
x = -2 ± √(4 + 96)
2
x = -2 ± √(100)
 2
x = -2 ± 10
 2
x = -1 ± 5
x = -1 + 5 U x = -1 - 5
x = 4 U x = -6

Answer 2

Since both sides has same factor (x+6), we can set (x+6) equal to 0.

So we would have one of solution x = -6. (because this would have us x·0 = 4·0 )

Now when x is NOT equal to -6, we can divide both sides by (x+6), leaving us

x = 4

So answer is x = -6 or 4.