Solve by factorisation: 2(x^2) - 5x - 12 = 0

First step is to multiply coefficient of first term (2) with the constant (-12) to enable us to split the middle term.2*(-12) = -24, therefore we need to find two numbers that multiply to -24, and add to give the coefficient of the second term (-5). These two numbers are -8 and 3 as these numbers add to give -5 and multiply to give -24. Therefore we can split the middle term: 2x² - 8x + 3x - 12 = 0By factorising:2x(x - 4) + 3(x - 4) = 0, (x - 4)(2x + 3) = 0.If (x - 4) = 0, x = 4.If (2x + 3) = 0, x = - 1.5.Therefore, solutions for x for this quadratic equation are x = 4, -1.5.