(m+2)(2m+3)=(m+2)(m+2)

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Solution for (m+2)(2m+3)=(m+2)(m+2) equation: 


Simplifying
(m + 2)(2m + 3) = (m + 2)(m + 2)

Reorder the terms:
(2 + m)(2m + 3) = (m + 2)(m + 2)

Reorder the terms:
(2 + m)(3 + 2m) = (m + 2)(m + 2)

Multiply (2 + m) * (3 + 2m)
(2(3 + 2m) + m(3 + 2m)) = (m + 2)(m + 2)
((3 * 2 + 2m * 2) + m(3 + 2m)) = (m + 2)(m + 2)
((6 + 4m) + m(3 + 2m)) = (m + 2)(m + 2)
(6 + 4m + (3 * m + 2m * m)) = (m + 2)(m + 2)
(6 + 4m + (3m + 2m2)) = (m + 2)(m + 2)

Combine like terms: 4m + 3m = 7m
(6 + 7m + 2m2) = (m + 2)(m + 2)

Reorder the terms:
6 + 7m + 2m2 = (2 + m)(m + 2)

Reorder the terms:
6 + 7m + 2m2 = (2 + m)(2 + m)

Multiply (2 + m) * (2 + m)
6 + 7m + 2m2 = (2(2 + m) + m(2 + m))
6 + 7m + 2m2 = ((2 * 2 + m * 2) + m(2 + m))
6 + 7m + 2m2 = ((4 + 2m) + m(2 + m))
6 + 7m + 2m2 = (4 + 2m + (2 * m + m * m))
6 + 7m + 2m2 = (4 + 2m + (2m + m2))

Combine like terms: 2m + 2m = 4m
6 + 7m + 2m2 = (4 + 4m + m2)

Solving
6 + 7m + 2m2 = 4 + 4m + m2

Solving for variable 'm'.

Reorder the terms:
6 + -4 + 7m + -4m + 2m2 + -1m2 = 4 + 4m + m2 + -4 + -4m + -1m2

Combine like terms: 6 + -4 = 2
2 + 7m + -4m + 2m2 + -1m2 = 4 + 4m + m2 + -4 + -4m + -1m2

Combine like terms: 7m + -4m = 3m
2 + 3m + 2m2 + -1m2 = 4 + 4m + m2 + -4 + -4m + -1m2

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

Reorder the terms:
2 + 3m + 1m2 = 4 + -4 + 4m + -4m + m2 + -1m2

Combine like terms: 4 + -4 = 0
2 + 3m + 1m2 = 0 + 4m + -4m + m2 + -1m2
2 + 3m + 1m2 = 4m + -4m + m2 + -1m2

Combine like terms: 4m + -4m = 0
2 + 3m + 1m2 = 0 + m2 + -1m2
2 + 3m + 1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
2 + 3m + 1m2 = 0

Factor a trinomial.
(2 + m)(1 + m) = 0


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

Simplifying
2 + m = 0

Solving
2 + m = 0

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

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

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

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

Simplifying
m = -2

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

Simplifying
1 + m = 0

Solving
1 + m = 0

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

Add '-1' to each side of the equation.
1 + -1 + m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + m = 0 + -1
m = 0 + -1

Combine like terms: 0 + -1 = -1
m = -1

Simplifying
m = -1
Solution
m = {-2, -1}

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