Solve by factoring (no "c" term-GCF) 0=3x^2+10x

Question

Please explain all the steps. There can be 2 answers

Answer 1

3x^2 +10x = 0

x(3x +10) = 0

set each factor =0

x=0

3x+10=0

3x =-10

x =-10/3

Answer 2

To solve this equation, which is quadratic since the highest power is 2, you must make sure every term is on one side of the equation and the other side is 0.

Our equation already is in this form, so you do not need to move any terms across the equal sign.

0=3x^2+10x

To factor, you should always try to factor out a GCF, or greatest common factor. So, if you look at the 3 and the 10, the only divisor of both is 1, so you can factor a 1 out, which is the same as leaving it alone. Now, focus on the x^2 and the x, which is really x^1. The greatest common factors is the most amount of x's that both terms share. How many do they share? Only 1. So, finding the GCF means finding the lowest exponent of both.

When you factor out an x, you get 0 = x(3x +10).

Now, the Zero Factor Property says you should set all terms that are multiplied each equal to 0. So, you have x = 0 or 3x + 10 = 0. If you solve the first one, you really don't do anything because x = 0 is already solved. To solve 3x + 10 = 0, subtract 10 from both sides to get 3x = -10. Then, devide both sides by 3 to get x = -10/3.

Thus, the answers, which you write in a solution set usually, are {0, -10/3}. These two values, if you plug them into the original equation for x, make the equality true. Try it to see!

And that's all there is to it!