Math problem, solve by factoring?

Question

6x^2 + x - 15 = 0

Please explain each step.

Answer 1

=(2x-3)(3x+5)=0

2x-3=0, x= 3/2

3x+5=0, x= -5/3

Answer 2

Given Ax^2 + Bx + C = 0, to factor, you would first find 2 numbers such that they multiply to AC and add up to B.

In this case, 2 numbers that multiply to 6*(-15) = -90 and add up to 1 is:

10, -9

So now, you rewrite the +x as

6x^2 - 9x + 10x - 15 = 0 (Note that -9x + 10x = x so you have not changed the original equation - Called decomposition)

Now, you factor the first 2 terms, and the last 2 terms to get:

3x(2x - 3) + 5(2x - 3) = 0

Pulled 3x out of the first 2 terms, and 5 out of the last 2 terms.

Now, notice that (2x - 3) is a common factor in both terms, so factor that out to get:

(2x - 3)(3x + 5) = 0

Now, to solve, when AB = 0, either A = 0 or B = 0.

Case 1: 2x - 3 = 0 implies x = 3/2

Case 2: 3x + 5 = 0 implies x = -5/3

This is the technique to solve all quadratics.

Good luck.

Answer 3

(2x-3)(3x+5)=0

2x*3x = 6x^2

2x*5 -3*3x = 1x

+3*5 = -15

by the zero property either 2x-3=0  or 3x+5=0

if 2x-3=0, then  x= 3/2

if 3x+5=0, x= -5/3