45k^2+37k-176=-8+4k

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Solution for 45k^2+37k-176=-8+4k equation: 


Simplifying
45k2 + 37k + -176 = -8 + 4k

Reorder the terms:
-176 + 37k + 45k2 = -8 + 4k

Solving
-176 + 37k + 45k2 = -8 + 4k

Solving for variable 'k'.

Reorder the terms:
-176 + 8 + 37k + -4k + 45k2 = -8 + 4k + 8 + -4k

Combine like terms: -176 + 8 = -168
-168 + 37k + -4k + 45k2 = -8 + 4k + 8 + -4k

Combine like terms: 37k + -4k = 33k
-168 + 33k + 45k2 = -8 + 4k + 8 + -4k

Reorder the terms:
-168 + 33k + 45k2 = -8 + 8 + 4k + -4k

Combine like terms: -8 + 8 = 0
-168 + 33k + 45k2 = 0 + 4k + -4k
-168 + 33k + 45k2 = 4k + -4k

Combine like terms: 4k + -4k = 0
-168 + 33k + 45k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-56 + 11k + 15k2) = 0

Factor a trinomial.
3((-7 + -3k)(8 + -5k)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -3k)' equal to zero and attempt to solve:

Simplifying
-7 + -3k = 0

Solving
-7 + -3k = 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 + -3k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3k = 0 + 7
-3k = 0 + 7

Combine like terms: 0 + 7 = 7
-3k = 7

Divide each side by '-3'.
k = -2.333333333

Simplifying
k = -2.333333333

Subproblem 2
Set the factor '(8 + -5k)' equal to zero and attempt to solve:

Simplifying
8 + -5k = 0

Solving
8 + -5k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5k = 0 + -8
-5k = 0 + -8

Combine like terms: 0 + -8 = -8
-5k = -8

Divide each side by '-5'.
k = 1.6

Simplifying
k = 1.6
Solution
k = {-2.333333333, 1.6}

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