We are looking for a factorization like
6x² + 7x - 5 = (_x + _)(_x - _)
where we need to fill in the numbers in the blanks. Since the first and third blanks multiply to 6, they have to be 1 and 6 or 2 and 3. Similarly, the second and fourth blanks multiply to 5 so they must be 1 and 5. By trial and error, we arrive at the factorization
6x² + 7x - 5 = (2x - 1)(3x + 5).
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(6x - 1)(6x - 1)
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: -2 plus or minus i times the square root of 17.x = -2 + 4.123105625617661ix = -2 - 4.123105625617661iwhere i is the square root of negative one.
(3x - 4)(2x^2 + 6x + 5)
With great difficulty not knowing if 6x and 27 are plus or minus
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: -3 plus or minus i, where i is the square root of negative 1.