1. x^2+8=-6x
x^2 + 8 + 6x = 0 (we have to move all the terms to one side and because they are equal, we can set the answer to 0)
x^2+ 4x + 2x + 8 = 0 (factor the expressions to get rid of the x squared in the next step)
x times (x + 4) + 2(x + 4) = 0
(x + 4) x (x + 2) = 0
x + 4 = 0
x + 2 = 0
Therefore, x = -4, x = -2.
2. x^2+5x=84
x^2 + 5x - 84 = 0
x^2 + 12x - 7x - 84 = 0
x(x + 12) - 7(x + 12) = 0
(x + 12)(x - 7) = 0
x + 12 = 0
x - 7 = 0
x = -12
x = 7
Therefore x = -12, x = 7.
3. (2x-1)(5x+3)=0
This already has most of the steps done, so we just need to split into possible cases
2x - 1 = 0 and 5x + 3 = 0
add one and minus three on both sides
2x = 1 and 5x = -3
divide by two and five on both sides
x = 1/2 and x = -3/5
Those are your answers!
Hope I helped!
