7n(7n+2)=8

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Solution for 7n(7n+2)=8 equation:


Simplifying
7n(7n + 2) = 8

Reorder the terms:
7n(2 + 7n) = 8
(2 * 7n + 7n * 7n) = 8
(14n + 49n2) = 8

Solving
14n + 49n2 = 8

Solving for variable 'n'.

Reorder the terms:
-8 + 14n + 49n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 14n + 49n2 = 0

Factor a trinomial.
(-4 + -7n)(2 + -7n) = 0

Subproblem 1

Set the factor '(-4 + -7n)' equal to zero and attempt to solve: Simplifying -4 + -7n = 0 Solving -4 + -7n = 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 + -7n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7n = 0 + 4 -7n = 0 + 4 Combine like terms: 0 + 4 = 4 -7n = 4 Divide each side by '-7'. n = -0.5714285714 Simplifying n = -0.5714285714

Subproblem 2

Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857

Solution

n = {-0.5714285714, 0.2857142857}

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