In an equation, both sides of the equal sign represent the same number, once all the math is done. An equals sign is like a see-saw: if an extra person gets on one side, then someone who weighs the same has to jump on the other side to keep the see-saw level. So you can add, subtract, multiply, or divide any number to one side of the equation as long as you do the exact same thing to the other side.
So, to solve for x in 5x + 3 = -12, we want to get x all alone on one side.
5x + 3 = -12
5x + 3 - 3 = -12 - 3 Subtract 3 from both sides
5x = -15 Simplify
5x/5 = -15/5 Divide both sides by 5
x = -3
Check the math:
5*(-3) + 3 =? -12
-15 + 3 =? -12
-12 = -12 check.