Getting an Equation to equal zero!

[_sophie_]

I have posted another maths question which I need help on for my final exam! Please check that out too if you can!

The 'hex' numbers form a sequence of positive integers. The nth 'hex' number is given by 1-3n+3n².
61 is a 'hex' number. Which one is it in the sequence?

Ok, so you have to get 1-3n+3n² to equal 0, but how?! I am so confused as to how you get an equation to equal 0. Please help! Show me working if you can as I am really not good at maths but find it easier to understand if you show me working for each line!!
Thanks.

[bibblebub]

1 - 3n + 3n² = 61

take 61 from both sides (and re-arrange the order of terms): 3n² - 3n - 60 = 0

divide by 3: n² - n + 20 = 0

factorise: (n + 4)(n - 5) = 0

therefore the two solutions are n = -4 and n = +5

you are after positive integers, so the answer is n = 5

[bibblebub]

^^^middle equation should be: divide by 3: n² - n - 20 = 0

[factor-fiction]

Same answer as bibblebub- I just took time to do it in Word and copy across.

Start with 1 - 3n + 3n² = 61

I'll show as many steps now as possible

• Subtract 1 from both sides: 3n² - 3n =60

• Divide both sides by 3: n² - n = 20
• Take 20 from both sides: n² - n - 20 =0
• Factorise: (n + 4)(n - 5) = 0
• So solutions are n = -4 and n = +5 (since either makes one of the brackets and hence the total calculation =0

Ignore n = -4 as it's negative and you want postive values. So n = 5

[_sophie_]

Thank you SO much! I get it now. God, I feel so stupid.. obviously you take away 61 to get 0. Haha, thank you!