x + 8 = −x2 + 4x + 12

• ramaaabdou: you bring all xs on one side then you solve as quadratic analysis.
  [tex]x + 8 + {x}^{2} - 4x - 12 = 0[/tex]
  [tex] {x}^{2} - 3x - 4 = 0[/tex]
  so you can simplify into
  [tex](x + 1)(x - 4) = 0[/tex]
  *Note that here 4 took the negative sign and 1 took the positive sign, as you want to numbers that if multiplied will give -4 and when added will give -3, and these are (-4 and 1)*
  
  so now you can simply say that, for the equation to equal 0, x should be -1 or 4.
  You can always substitute to make sure of your calculations.
  
  Hope this helps.
• pi314:

  The answer is x=−1 or x=4.

  Combine like terms and divide!