6m+(m-2)(m+7)+3=

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Solution for 6m+(m-2)(m+7)+3= equation: 


Simplifying
6m + (m + -2)(m + 7) + 3 = 0

Reorder the terms:
6m + (-2 + m)(m + 7) + 3 = 0

Reorder the terms:
6m + (-2 + m)(7 + m) + 3 = 0

Multiply (-2 + m) * (7 + m)
6m + (-2(7 + m) + m(7 + m)) + 3 = 0
6m + ((7 * -2 + m * -2) + m(7 + m)) + 3 = 0
6m + ((-14 + -2m) + m(7 + m)) + 3 = 0
6m + (-14 + -2m + (7 * m + m * m)) + 3 = 0
6m + (-14 + -2m + (7m + m2)) + 3 = 0

Combine like terms: -2m + 7m = 5m
6m + (-14 + 5m + m2) + 3 = 0

Reorder the terms:
-14 + 3 + 6m + 5m + m2 = 0

Combine like terms: -14 + 3 = -11
-11 + 6m + 5m + m2 = 0

Combine like terms: 6m + 5m = 11m
-11 + 11m + m2 = 0

Solving
-11 + 11m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 11m + 11 + m2 = 0 + 11

Reorder the terms:
-11 + 11 + 11m + m2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 11m + m2 = 0 + 11
11m + m2 = 0 + 11

Combine like terms: 0 + 11 = 11
11m + m2 = 11

The m term is 11m.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11m + 30.25 + m2 = 11 + 30.25

Reorder the terms:
30.25 + 11m + m2 = 11 + 30.25

Combine like terms: 11 + 30.25 = 41.25
30.25 + 11m + m2 = 41.25

Factor a perfect square on the left side:
(m + 5.5)(m + 5.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(m + 5.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
m + 5.5 = 6.422616289

Simplifying
m + 5.5 = 6.422616289

Reorder the terms:
5.5 + m = 6.422616289

Solving
5.5 + m = 6.422616289

Solving for variable 'm'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + m = 6.422616289 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + m = 6.422616289 + -5.5
m = 6.422616289 + -5.5

Combine like terms: 6.422616289 + -5.5 = 0.922616289
m = 0.922616289

Simplifying
m = 0.922616289


Subproblem 2
m + 5.5 = -6.422616289

Simplifying
m + 5.5 = -6.422616289

Reorder the terms:
5.5 + m = -6.422616289

Solving
5.5 + m = -6.422616289

Solving for variable 'm'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + m = -6.422616289 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + m = -6.422616289 + -5.5
m = -6.422616289 + -5.5

Combine like terms: -6.422616289 + -5.5 = -11.922616289
m = -11.922616289

Simplifying
m = -11.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.922616289, -11.922616289}

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