(m+4)(2m+3)=22+10m

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Solution for (m+4)(2m+3)=22+10m equation: 


Simplifying
(m + 4)(2m + 3) = 22 + 10m

Reorder the terms:
(4 + m)(2m + 3) = 22 + 10m

Reorder the terms:
(4 + m)(3 + 2m) = 22 + 10m

Multiply (4 + m) * (3 + 2m)
(4(3 + 2m) + m(3 + 2m)) = 22 + 10m
((3 * 4 + 2m * 4) + m(3 + 2m)) = 22 + 10m
((12 + 8m) + m(3 + 2m)) = 22 + 10m
(12 + 8m + (3 * m + 2m * m)) = 22 + 10m
(12 + 8m + (3m + 2m2)) = 22 + 10m

Combine like terms: 8m + 3m = 11m
(12 + 11m + 2m2) = 22 + 10m

Solving
12 + 11m + 2m2 = 22 + 10m

Solving for variable 'm'.

Reorder the terms:
12 + -22 + 11m + -10m + 2m2 = 22 + 10m + -22 + -10m

Combine like terms: 12 + -22 = -10
-10 + 11m + -10m + 2m2 = 22 + 10m + -22 + -10m

Combine like terms: 11m + -10m = 1m
-10 + 1m + 2m2 = 22 + 10m + -22 + -10m

Reorder the terms:
-10 + 1m + 2m2 = 22 + -22 + 10m + -10m

Combine like terms: 22 + -22 = 0
-10 + 1m + 2m2 = 0 + 10m + -10m
-10 + 1m + 2m2 = 10m + -10m

Combine like terms: 10m + -10m = 0
-10 + 1m + 2m2 = 0

Factor a trinomial.
(-5 + -2m)(2 + -1m) = 0


Subproblem 1
Set the factor '(-5 + -2m)' equal to zero and attempt to solve:

Simplifying
-5 + -2m = 0

Solving
-5 + -2m = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2m = 0 + 5
-2m = 0 + 5

Combine like terms: 0 + 5 = 5
-2m = 5

Divide each side by '-2'.
m = -2.5

Simplifying
m = -2.5

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

Simplifying
2 + -1m = 0

Solving
2 + -1m = 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 + -1m = 0 + -2

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

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

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Solution
m = {-2.5, 2}

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