What are the solutions of - x^2+4x=x-4

x = - 1 and x = 4

Step-by-step explanation:

Step 1: Get everything to one side of the equation so it's set equal to zero ...

-x² + 4x = x - 4 becomes ...

-x² + 3x + 4 = 0 (subtract x and add 4 to both sides)

x² - 3x - 4 = 0 (divide both sides by - 1, we want the x² term to be positive)

(x - 4) (x + 1) = 0 (factor)

so

x - 4 = 0, then x = 4

and

x + 1 = 0, then x = - 1