Solve the equation. n(3n - 2) = 40

Ann Tice

Ann Tice

Answered question

2021-11-18

Solve the equation.
n(3n - 2) = 40

Answer & Explanation

Traidnew

Traidnew

Beginner2021-11-19Added 14 answers

Step 1
Separate the unknown variable on one side of the equation.
Given equation is quadratic equation.
Derivative of the function decides whether the function is increasing or decreasing. If the first derivative is positive, function is increasing in that particular interval. If it is negative, function is decreasing for that particular interval.
Step 2
n(3n-2)=40
3n22n=40
3n22n40=0
(n-4)(3n+10)=0
n=4,103
Traidnew

Traidnew

Beginner2021-11-20Added 14 answers

Simplifying
n(3n + -2) = 40
Reorder the terms:
n(-2 + 3n) = 40
(-2 * n + 3n * n) = 40
(2n+3n2)=40
Solving
2n+3n2=40
Solving for variable 'n'.
Reorder the terms:
40+2n+3n2=40+40
Combine like terms: 40 + -40 = 0
40+2n+3n2=0
Factor a trinomial.
(-10 + -3n)(4 + -1n) = 0
Set the factor '(-10 + -3n)' equal to zero and attempt to solve:
Simplifying
-10 + -3n = 0
Solving
-10 + -3n = 0
Move all terms containing n to the left, all other terms to the right.
Add '10' to each side of the equation.
-10 + 10 + -3n = 0 + 10
Combine like terms: -10 + 10 = 0
0 + -3n = 0 + 10
-3n = 0 + 10
Combine like terms: 0 + 10 = 10
-3n = 10
Divide each side by '-3'.
n=103
Set the factor '(4 + -1n)' equal to zero and attempt to solve:
Simplifying
4 + -1n = 0
Solving
4 + -1n = 0
Move all terms containing n to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4
Combine like terms: 0 + -4 = -4
-1n = -4
Divide each side by '-1'.
n = 4
Result: n=4,n=103

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