4m(3m+6)+7(1+8m)=0

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Solution for 4m(3m+6)+7(1+8m)=0 equation: 


Simplifying
4m(3m + 6) + 7(1 + 8m) = 0

Reorder the terms:
4m(6 + 3m) + 7(1 + 8m) = 0
(6 * 4m + 3m * 4m) + 7(1 + 8m) = 0
(24m + 12m2) + 7(1 + 8m) = 0
24m + 12m2 + (1 * 7 + 8m * 7) = 0
24m + 12m2 + (7 + 56m) = 0

Reorder the terms:
7 + 24m + 56m + 12m2 = 0

Combine like terms: 24m + 56m = 80m
7 + 80m + 12m2 = 0

Solving
7 + 80m + 12m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
0.5833333333 + 6.666666667m + m2 = 0

Move the constant term to the right:

Add '-0.5833333333' to each side of the equation.
0.5833333333 + 6.666666667m + -0.5833333333 + m2 = 0 + -0.5833333333

Reorder the terms:
0.5833333333 + -0.5833333333 + 6.666666667m + m2 = 0 + -0.5833333333

Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000
0.0000000000 + 6.666666667m + m2 = 0 + -0.5833333333
6.666666667m + m2 = 0 + -0.5833333333

Combine like terms: 0 + -0.5833333333 = -0.5833333333
6.666666667m + m2 = -0.5833333333

The m term is 6.666666667m.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667m + 11.11111112 + m2 = -0.5833333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667m + m2 = -0.5833333333 + 11.11111112

Combine like terms: -0.5833333333 + 11.11111112 = 10.5277777867
11.11111112 + 6.666666667m + m2 = 10.5277777867

Factor a perfect square on the left side:
(m + 3.333333334)(m + 3.333333334) = 10.5277777867

Calculate the square root of the right side: 3.244653724

Break this problem into two subproblems by setting 
(m + 3.333333334) equal to 3.244653724 and -3.244653724.


Subproblem 1
m + 3.333333334 = 3.244653724

Simplifying
m + 3.333333334 = 3.244653724

Reorder the terms:
3.333333334 + m = 3.244653724

Solving
3.333333334 + m = 3.244653724

Solving for variable 'm'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + m = 3.244653724 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + m = 3.244653724 + -3.333333334
m = 3.244653724 + -3.333333334

Combine like terms: 3.244653724 + -3.333333334 = -0.08867961
m = -0.08867961

Simplifying
m = -0.08867961


Subproblem 2
m + 3.333333334 = -3.244653724

Simplifying
m + 3.333333334 = -3.244653724

Reorder the terms:
3.333333334 + m = -3.244653724

Solving
3.333333334 + m = -3.244653724

Solving for variable 'm'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + m = -3.244653724 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + m = -3.244653724 + -3.333333334
m = -3.244653724 + -3.333333334

Combine like terms: -3.244653724 + -3.333333334 = -6.577987058
m = -6.577987058

Simplifying
m = -6.577987058


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.08867961, -6.577987058}

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