3m(m-3)-6(m-5)=2m^2-4

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Solution for 3m(m-3)-6(m-5)=2m^2-4 equation:


Simplifying
3m(m + -3) + -6(m + -5) = 2m2 + -4

Reorder the terms:
3m(-3 + m) + -6(m + -5) = 2m2 + -4
(-3 * 3m + m * 3m) + -6(m + -5) = 2m2 + -4
(-9m + 3m2) + -6(m + -5) = 2m2 + -4

Reorder the terms:
-9m + 3m2 + -6(-5 + m) = 2m2 + -4
-9m + 3m2 + (-5 * -6 + m * -6) = 2m2 + -4
-9m + 3m2 + (30 + -6m) = 2m2 + -4

Reorder the terms:
30 + -9m + -6m + 3m2 = 2m2 + -4

Combine like terms: -9m + -6m = -15m
30 + -15m + 3m2 = 2m2 + -4

Reorder the terms:
30 + -15m + 3m2 = -4 + 2m2

Solving
30 + -15m + 3m2 = -4 + 2m2

Solving for variable 'm'.

Reorder the terms:
30 + 4 + -15m + 3m2 + -2m2 = -4 + 2m2 + 4 + -2m2

Combine like terms: 30 + 4 = 34
34 + -15m + 3m2 + -2m2 = -4 + 2m2 + 4 + -2m2

Combine like terms: 3m2 + -2m2 = 1m2
34 + -15m + 1m2 = -4 + 2m2 + 4 + -2m2

Reorder the terms:
34 + -15m + 1m2 = -4 + 4 + 2m2 + -2m2

Combine like terms: -4 + 4 = 0
34 + -15m + 1m2 = 0 + 2m2 + -2m2
34 + -15m + 1m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
34 + -15m + 1m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -15m + -34 + m2 = 0 + -34

Reorder the terms:
34 + -34 + -15m + m2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -15m + m2 = 0 + -34
-15m + m2 = 0 + -34

Combine like terms: 0 + -34 = -34
-15m + m2 = -34

The m term is -15m.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15m + 56.25 + m2 = -34 + 56.25

Reorder the terms:
56.25 + -15m + m2 = -34 + 56.25

Combine like terms: -34 + 56.25 = 22.25
56.25 + -15m + m2 = 22.25

Factor a perfect square on the left side:
(m + -7.5)(m + -7.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(m + -7.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

m + -7.5 = 4.716990566 Simplifying m + -7.5 = 4.716990566 Reorder the terms: -7.5 + m = 4.716990566 Solving -7.5 + m = 4.716990566 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + m = 4.716990566 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = 4.716990566 + 7.5 m = 4.716990566 + 7.5 Combine like terms: 4.716990566 + 7.5 = 12.216990566 m = 12.216990566 Simplifying m = 12.216990566

Subproblem 2

m + -7.5 = -4.716990566 Simplifying m + -7.5 = -4.716990566 Reorder the terms: -7.5 + m = -4.716990566 Solving -7.5 + m = -4.716990566 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + m = -4.716990566 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = -4.716990566 + 7.5 m = -4.716990566 + 7.5 Combine like terms: -4.716990566 + 7.5 = 2.783009434 m = 2.783009434 Simplifying m = 2.783009434

Solution

The solution to the problem is based on the solutions from the subproblems. m = {12.216990566, 2.783009434}

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