-7m(3m+7)+3(m+1)=

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Solution for -7m(3m+7)+3(m+1)= equation:


Simplifying
-7m(3m + 7) + 3(m + 1) = 0

Reorder the terms:
-7m(7 + 3m) + 3(m + 1) = 0
(7 * -7m + 3m * -7m) + 3(m + 1) = 0
(-49m + -21m2) + 3(m + 1) = 0

Reorder the terms:
-49m + -21m2 + 3(1 + m) = 0
-49m + -21m2 + (1 * 3 + m * 3) = 0
-49m + -21m2 + (3 + 3m) = 0

Reorder the terms:
3 + -49m + 3m + -21m2 = 0

Combine like terms: -49m + 3m = -46m
3 + -46m + -21m2 = 0

Solving
3 + -46m + -21m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-0.1428571429 + 2.19047619m + m2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 2.19047619m + 0.1428571429 + m2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 2.19047619m + m2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 2.19047619m + m2 = 0 + 0.1428571429
2.19047619m + m2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
2.19047619m + m2 = 0.1428571429

The m term is 2.19047619m.  Take half its coefficient (1.095238095).
Square it (1.199546485) and add it to both sides.

Add '1.199546485' to each side of the equation.
2.19047619m + 1.199546485 + m2 = 0.1428571429 + 1.199546485

Reorder the terms:
1.199546485 + 2.19047619m + m2 = 0.1428571429 + 1.199546485

Combine like terms: 0.1428571429 + 1.199546485 = 1.3424036279
1.199546485 + 2.19047619m + m2 = 1.3424036279

Factor a perfect square on the left side:
(m + 1.095238095)(m + 1.095238095) = 1.3424036279

Calculate the square root of the right side: 1.158621434

Break this problem into two subproblems by setting 
(m + 1.095238095) equal to 1.158621434 and -1.158621434.

Subproblem 1

m + 1.095238095 = 1.158621434 Simplifying m + 1.095238095 = 1.158621434 Reorder the terms: 1.095238095 + m = 1.158621434 Solving 1.095238095 + m = 1.158621434 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.095238095' to each side of the equation. 1.095238095 + -1.095238095 + m = 1.158621434 + -1.095238095 Combine like terms: 1.095238095 + -1.095238095 = 0.000000000 0.000000000 + m = 1.158621434 + -1.095238095 m = 1.158621434 + -1.095238095 Combine like terms: 1.158621434 + -1.095238095 = 0.063383339 m = 0.063383339 Simplifying m = 0.063383339

Subproblem 2

m + 1.095238095 = -1.158621434 Simplifying m + 1.095238095 = -1.158621434 Reorder the terms: 1.095238095 + m = -1.158621434 Solving 1.095238095 + m = -1.158621434 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.095238095' to each side of the equation. 1.095238095 + -1.095238095 + m = -1.158621434 + -1.095238095 Combine like terms: 1.095238095 + -1.095238095 = 0.000000000 0.000000000 + m = -1.158621434 + -1.095238095 m = -1.158621434 + -1.095238095 Combine like terms: -1.158621434 + -1.095238095 = -2.253859529 m = -2.253859529 Simplifying m = -2.253859529

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.063383339, -2.253859529}

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