2(k-5)(k-5)+7=15

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Solution for 2(k-5)(k-5)+7=15 equation: 


Simplifying
2(k + -5)(k + -5) + 7 = 15

Reorder the terms:
2(-5 + k)(k + -5) + 7 = 15

Reorder the terms:
2(-5 + k)(-5 + k) + 7 = 15

Multiply (-5 + k) * (-5 + k)
2(-5(-5 + k) + k(-5 + k)) + 7 = 15
2((-5 * -5 + k * -5) + k(-5 + k)) + 7 = 15
2((25 + -5k) + k(-5 + k)) + 7 = 15
2(25 + -5k + (-5 * k + k * k)) + 7 = 15
2(25 + -5k + (-5k + k2)) + 7 = 15

Combine like terms: -5k + -5k = -10k
2(25 + -10k + k2) + 7 = 15
(25 * 2 + -10k * 2 + k2 * 2) + 7 = 15
(50 + -20k + 2k2) + 7 = 15

Reorder the terms:
50 + 7 + -20k + 2k2 = 15

Combine like terms: 50 + 7 = 57
57 + -20k + 2k2 = 15

Solving
57 + -20k + 2k2 = 15

Solving for variable 'k'.

Reorder the terms:
57 + -15 + -20k + 2k2 = 15 + -15

Combine like terms: 57 + -15 = 42
42 + -20k + 2k2 = 15 + -15

Combine like terms: 15 + -15 = 0
42 + -20k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -10k + k2) = 0

Factor a trinomial.
2((3 + -1k)(7 + -1k)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3

Subproblem 2
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
Solution
k = {3, 7}

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