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  

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step-by-step explanation: