The first coefficient is 2. The last term is -21. They multiply to -42. We need to find two numbers that multiply to -42 and add to 1. The "1" refers to the coefficient of the middle x term. Two such numbers that do this are 7 and -6
7 times -6 = -42
7 plus -6 = 1
So we will break up the middle "x" term into 7x + (-6x) or 7x - 6x.
Then we factor by grouping.
2x^2 + x - 21 = 0
2x^2 + 7x - 6x - 21 = 0
(2x^2 + 7x) + (-6x - 21) = 0
x(2x + 7) - 3(2x + 7) = 0
(x - 3)(2x + 7) = 0
x-3 = 0 or 2x+7 = 0
x = 3 or 2x = -7
x = 3 or x = -7/2
Answers: x = 3 or x = -7/2
note: the fraction -7/2 turns into the decimal form -3.5
