4k^2-126=-10k

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Solution for 4k^2-126=-10k equation:


Simplifying
4k2 + -126 = -10k

Reorder the terms:
-126 + 4k2 = -10k

Solving
-126 + 4k2 = -10k

Solving for variable 'k'.

Reorder the terms:
-126 + 10k + 4k2 = -10k + 10k

Combine like terms: -10k + 10k = 0
-126 + 10k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + 5k + 2k2) = 0

Factor a trinomial.
2((-7 + -1k)(9 + -2k)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -1k)' equal to zero and attempt to solve: Simplifying -7 + -1k = 0 Solving -7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1k = 0 + 7 -1k = 0 + 7 Combine like terms: 0 + 7 = 7 -1k = 7 Divide each side by '-1'. k = -7 Simplifying k = -7

Subproblem 2

Set the factor '(9 + -2k)' equal to zero and attempt to solve: Simplifying 9 + -2k = 0 Solving 9 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2k = 0 + -9 -2k = 0 + -9 Combine like terms: 0 + -9 = -9 -2k = -9 Divide each side by '-2'. k = 4.5 Simplifying k = 4.5

Solution

k = {-7, 4.5}

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