Consider the following quadratic equation:
12x^2=−2x
Step 1 of 2 : Using the standard form ax2+bx+c=0
of the given quadratic equation, factor the left hand side of the equation into two linear factors.
To factor the left-hand side of the equation, 12x^2 = -2x, we need to find two linear factors that when multiplied together give us 12x^2 and when added or subtracted give us -2x.
We can start by factoring out the greatest common factor (GCF) from both terms, which in this case is 2x:
2x(6x + 1) = -2x
Next, we can rearrange the equation to have all terms on one side:
2x(6x + 1) + 2x = 0
Now, we can factor out the GCF, 2x, from both terms on the left-hand side:
2x(6x + 1 + 1) = 0
Simplifying further:
2x(6x + 2) = 0
So, the left-hand side of the equation is factored into two linear factors:
2x(6x + 2) = 0