Answer:
x = -3.5 or x = 1.7
Step-by-step explanation:
Start by factoring the left side.
We need to find two numbers that have a product of -210 (6 * -35) and a sum of 11...
-10*21=-210
-10+21=11
We can rewrite 11x as -10x+21x...
[tex]6x^2-10x+21x-35=0[/tex]
Then, factor the first and second half of the left side individually:
[tex]2x(3x-5)+7(3x-5)=0[/tex]
Since 2x and 7 are both being multiplied by 3x-5, we can combine them to get:
[tex](3x-5)(2x+7)=0[/tex]
Divide the equation by 3x-5:
2x+7=0
Subtract 7 from both sides
2x=-7
Divide both sides by 2
x=-7/2=-3.5
Now, we also have to consider another answer, in which we divide the equation by 2x+7 instead of 3x-5:
3x-5=0
Add 5 to both sides
3x=5
Divide both sides by 3
x=5/3≈1.7
