3m^2-2m=4m^2+5+10

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Solution for 3m^2-2m=4m^2+5+10 equation: 


Simplifying
3m2 + -2m = 4m2 + 5 + 10

Reorder the terms:
-2m + 3m2 = 4m2 + 5 + 10

Reorder the terms:
-2m + 3m2 = 5 + 10 + 4m2

Combine like terms: 5 + 10 = 15
-2m + 3m2 = 15 + 4m2

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

Solving for variable 'm'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 2m + m2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(15 + 2m + m2)' equal to zero and attempt to solve:

Simplifying
15 + 2m + m2 = 0

Solving
15 + 2m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 2m + -15 + m2 = 0 + -15

Reorder the terms:
15 + -15 + 2m + m2 = 0 + -15

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

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

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = -15 + 1

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

Combine like terms: -15 + 1 = -14
1 + 2m + m2 = -14

Factor a perfect square on the left side:
(m + 1)(m + 1) = -14

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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