(4k+50)(k+7)=0

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Solution for (4k+50)(k+7)=0 equation: 


Simplifying
(4k + 50)(k + 7) = 0

Reorder the terms:
(50 + 4k)(k + 7) = 0

Reorder the terms:
(50 + 4k)(7 + k) = 0

Multiply (50 + 4k) * (7 + k)
(50(7 + k) + 4k * (7 + k)) = 0
((7 * 50 + k * 50) + 4k * (7 + k)) = 0
((350 + 50k) + 4k * (7 + k)) = 0
(350 + 50k + (7 * 4k + k * 4k)) = 0
(350 + 50k + (28k + 4k2)) = 0

Combine like terms: 50k + 28k = 78k
(350 + 78k + 4k2) = 0

Solving
350 + 78k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(175 + 39k + 2k2) = 0

Factor a trinomial.
2((25 + 2k)(7 + k)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 2k)' equal to zero and attempt to solve:

Simplifying
25 + 2k = 0

Solving
25 + 2k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-25' to each side of the equation.
25 + -25 + 2k = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 2k = 0 + -25
2k = 0 + -25

Combine like terms: 0 + -25 = -25
2k = -25

Divide each side by '2'.
k = -12.5

Simplifying
k = -12.5

Subproblem 2
Set the factor '(7 + k)' equal to zero and attempt to solve:

Simplifying
7 + k = 0

Solving
7 + k = 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 + k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + k = 0 + -7
k = 0 + -7

Combine like terms: 0 + -7 = -7
k = -7

Simplifying
k = -7
Solution
k = {-12.5, -7}

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