factorise 8x^2+14x-3

Sure, let's factorise the quadratic equation 8x^2 + 14x - 3 step by step.

Step 1: Multiply the coefficient of x^2 (which is 8) with the constant term (which is -3). The result is -24.

Step 2: Now, we need to find two numbers that multiply to -24 (from step 1) and add up to 14 (the coefficient of x). The numbers are 18 and -4 because 18*-4 = -24 and 18 - 4 = 14.

Step 3: Rewrite the middle term (14x) of the quadratic equation as the sum of the terms 18x and -4x. The equation becomes 8x^2 + 18x - 4x - 3.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us 2x(4x + 9) - 1(4x + 9).

Step 5: Notice that (4x + 9) is a common factor. By factoring out this common factor, we get (4x + 9)(2x - 1).

So, the factorised form of the quadratic equation 8x^2 + 14x - 3 is (4x + 9)(2x - 1).