(2m+1)x^2+2(m+3)x+(m+5)=0

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Solution for (2m+1)x^2+2(m+3)x+(m+5)=0 equation: 


Simplifying
(2m + 1) * x2 + 2(m + 3) * x + (m + 5) = 0

Reorder the terms:
(1 + 2m) * x2 + 2(m + 3) * x + (m + 5) = 0

Reorder the terms for easier multiplication:
x2(1 + 2m) + 2(m + 3) * x + (m + 5) = 0
(1 * x2 + 2m * x2) + 2(m + 3) * x + (m + 5) = 0

Reorder the terms:
(2mx2 + 1x2) + 2(m + 3) * x + (m + 5) = 0
(2mx2 + 1x2) + 2(m + 3) * x + (m + 5) = 0

Reorder the terms:
2mx2 + 1x2 + 2(3 + m) * x + (m + 5) = 0

Reorder the terms for easier multiplication:
2mx2 + 1x2 + 2x(3 + m) + (m + 5) = 0
2mx2 + 1x2 + (3 * 2x + m * 2x) + (m + 5) = 0

Reorder the terms:
2mx2 + 1x2 + (2mx + 6x) + (m + 5) = 0
2mx2 + 1x2 + (2mx + 6x) + (m + 5) = 0

Reorder the terms:
2mx2 + 1x2 + 2mx + 6x + (5 + m) = 0

Remove parenthesis around (5 + m)
2mx2 + 1x2 + 2mx + 6x + 5 + m = 0

Reorder the terms:
5 + m + 2mx + 2mx2 + 6x + 1x2 = 0

Solving
5 + m + 2mx + 2mx2 + 6x + 1x2 = 0

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + m + 2mx + 2mx2 + 6x + -5 + 1x2 = 0 + -5

Reorder the terms:
5 + -5 + m + 2mx + 2mx2 + 6x + 1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + m + 2mx + 2mx2 + 6x + 1x2 = 0 + -5
m + 2mx + 2mx2 + 6x + 1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
m + 2mx + 2mx2 + 6x + 1x2 = -5

Add '-6x' to each side of the equation.
m + 2mx + 2mx2 + 6x + -6x + 1x2 = -5 + -6x

Combine like terms: 6x + -6x = 0
m + 2mx + 2mx2 + 0 + 1x2 = -5 + -6x
m + 2mx + 2mx2 + 1x2 = -5 + -6x

Add '-1x2' to each side of the equation.
m + 2mx + 2mx2 + 1x2 + -1x2 = -5 + -6x + -1x2

Combine like terms: 1x2 + -1x2 = 0
m + 2mx + 2mx2 + 0 = -5 + -6x + -1x2
m + 2mx + 2mx2 = -5 + -6x + -1x2

Reorder the terms:
5 + m + 2mx + 2mx2 + 6x + x2 = -5 + -6x + -1x2 + 5 + 6x + x2

Reorder the terms:
5 + m + 2mx + 2mx2 + 6x + x2 = -5 + 5 + -6x + 6x + -1x2 + x2

Combine like terms: -5 + 5 = 0
5 + m + 2mx + 2mx2 + 6x + x2 = 0 + -6x + 6x + -1x2 + x2
5 + m + 2mx + 2mx2 + 6x + x2 = -6x + 6x + -1x2 + x2

Combine like terms: -6x + 6x = 0
5 + m + 2mx + 2mx2 + 6x + x2 = 0 + -1x2 + x2
5 + m + 2mx + 2mx2 + 6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
5 + m + 2mx + 2mx2 + 6x + x2 = 0

The solution to this equation could not be determined.

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