12k^2-60k=-75

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Solution for 12k^2-60k=-75 equation:


Simplifying
12k2 + -60k = -75

Reorder the terms:
-60k + 12k2 = -75

Solving
-60k + 12k2 = -75

Solving for variable 'k'.

Reorder the terms:
75 + -60k + 12k2 = -75 + 75

Combine like terms: -75 + 75 = 0
75 + -60k + 12k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -20k + 4k2) = 0

Factor a trinomial.
3((5 + -2k)(5 + -2k)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -2k)' equal to zero and attempt to solve: Simplifying 5 + -2k = 0 Solving 5 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2k = 0 + -5 -2k = 0 + -5 Combine like terms: 0 + -5 = -5 -2k = -5 Divide each side by '-2'. k = 2.5 Simplifying k = 2.5

Subproblem 2

Set the factor '(5 + -2k)' equal to zero and attempt to solve: Simplifying 5 + -2k = 0 Solving 5 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2k = 0 + -5 -2k = 0 + -5 Combine like terms: 0 + -5 = -5 -2k = -5 Divide each side by '-2'. k = 2.5 Simplifying k = 2.5

Solution

k = {2.5, 2.5}

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