-7m(-m-3)=45

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Solution for -7m(-m-3)=45 equation:


Simplifying
-7m(-1m + -3) = 45

Reorder the terms:
-7m(-3 + -1m) = 45
(-3 * -7m + -1m * -7m) = 45
(21m + 7m2) = 45

Solving
21m + 7m2 = 45

Solving for variable 'm'.

Reorder the terms:
-45 + 21m + 7m2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 21m + 7m2 = 0

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

Divide each side by '7'.
-6.428571429 + 3m + m2 = 0

Move the constant term to the right:

Add '6.428571429' to each side of the equation.
-6.428571429 + 3m + 6.428571429 + m2 = 0 + 6.428571429

Reorder the terms:
-6.428571429 + 6.428571429 + 3m + m2 = 0 + 6.428571429

Combine like terms: -6.428571429 + 6.428571429 = 0.000000000
0.000000000 + 3m + m2 = 0 + 6.428571429
3m + m2 = 0 + 6.428571429

Combine like terms: 0 + 6.428571429 = 6.428571429
3m + m2 = 6.428571429

The m term is 3m.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3m + 2.25 + m2 = 6.428571429 + 2.25

Reorder the terms:
2.25 + 3m + m2 = 6.428571429 + 2.25

Combine like terms: 6.428571429 + 2.25 = 8.678571429
2.25 + 3m + m2 = 8.678571429

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 8.678571429

Calculate the square root of the right side: 2.945941518

Break this problem into two subproblems by setting 
(m + 1.5) equal to 2.945941518 and -2.945941518.

Subproblem 1

m + 1.5 = 2.945941518 Simplifying m + 1.5 = 2.945941518 Reorder the terms: 1.5 + m = 2.945941518 Solving 1.5 + m = 2.945941518 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 2.945941518 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 2.945941518 + -1.5 m = 2.945941518 + -1.5 Combine like terms: 2.945941518 + -1.5 = 1.445941518 m = 1.445941518 Simplifying m = 1.445941518

Subproblem 2

m + 1.5 = -2.945941518 Simplifying m + 1.5 = -2.945941518 Reorder the terms: 1.5 + m = -2.945941518 Solving 1.5 + m = -2.945941518 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -2.945941518 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -2.945941518 + -1.5 m = -2.945941518 + -1.5 Combine like terms: -2.945941518 + -1.5 = -4.445941518 m = -4.445941518 Simplifying m = -4.445941518

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.445941518, -4.445941518}

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