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

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


Simplifying
m(2m + -7) = 3m2 + 3

Reorder the terms:
m(-7 + 2m) = 3m2 + 3
(-7 * m + 2m * m) = 3m2 + 3
(-7m + 2m2) = 3m2 + 3

Reorder the terms:
-7m + 2m2 = 3 + 3m2

Solving
-7m + 2m2 = 3 + 3m2

Solving for variable 'm'.

Reorder the terms:
-3 + -7m + 2m2 + -3m2 = 3 + 3m2 + -3 + -3m2

Combine like terms: 2m2 + -3m2 = -1m2
-3 + -7m + -1m2 = 3 + 3m2 + -3 + -3m2

Reorder the terms:
-3 + -7m + -1m2 = 3 + -3 + 3m2 + -3m2

Combine like terms: 3 + -3 = 0
-3 + -7m + -1m2 = 0 + 3m2 + -3m2
-3 + -7m + -1m2 = 3m2 + -3m2

Combine like terms: 3m2 + -3m2 = 0
-3 + -7m + -1m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7m + m2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 7m + m2)' equal to zero and attempt to solve:

Simplifying
3 + 7m + m2 = 0

Solving
3 + 7m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 7m + -3 + m2 = 0 + -3

Reorder the terms:
3 + -3 + 7m + m2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7m + m2 = 0 + -3
7m + m2 = 0 + -3

Combine like terms: 0 + -3 = -3
7m + m2 = -3

The m term is 7m.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7m + 12.25 + m2 = -3 + 12.25

Reorder the terms:
12.25 + 7m + m2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + 7m + m2 = 9.25

Factor a perfect square on the left side:
(m + 3.5)(m + 3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(m + 3.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
m + 3.5 = 3.041381265

Simplifying
m + 3.5 = 3.041381265

Reorder the terms:
3.5 + m = 3.041381265

Solving
3.5 + m = 3.041381265

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = 3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = 3.041381265 + -3.5
m = 3.041381265 + -3.5

Combine like terms: 3.041381265 + -3.5 = -0.458618735
m = -0.458618735

Simplifying
m = -0.458618735


Subproblem 2
m + 3.5 = -3.041381265

Simplifying
m + 3.5 = -3.041381265

Reorder the terms:
3.5 + m = -3.041381265

Solving
3.5 + m = -3.041381265

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = -3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = -3.041381265 + -3.5
m = -3.041381265 + -3.5

Combine like terms: -3.041381265 + -3.5 = -6.541381265
m = -6.541381265

Simplifying
m = -6.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.458618735, -6.541381265}
Solution
m = {-0.458618735, -6.541381265}

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