7k^2=31k-12

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Solution for 7k^2=31k-12 equation:


Simplifying
7k2 = 31k + -12

Reorder the terms:
7k2 = -12 + 31k

Solving
7k2 = -12 + 31k

Solving for variable 'k'.

Reorder the terms:
12 + -31k + 7k2 = -12 + 31k + 12 + -31k

Reorder the terms:
12 + -31k + 7k2 = -12 + 12 + 31k + -31k

Combine like terms: -12 + 12 = 0
12 + -31k + 7k2 = 0 + 31k + -31k
12 + -31k + 7k2 = 31k + -31k

Combine like terms: 31k + -31k = 0
12 + -31k + 7k2 = 0

Factor a trinomial.
(3 + -7k)(4 + -1k) = 0

Subproblem 1

Set the factor '(3 + -7k)' equal to zero and attempt to solve: Simplifying 3 + -7k = 0 Solving 3 + -7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7k = 0 + -3 -7k = 0 + -3 Combine like terms: 0 + -3 = -3 -7k = -3 Divide each side by '-7'. k = 0.4285714286 Simplifying k = 0.4285714286

Subproblem 2

Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4

Solution

k = {0.4285714286, 4}

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