(m+2)(3m+10)=3(m+5)+15

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Solution for (m+2)(3m+10)=3(m+5)+15 equation: 


Simplifying
(m + 2)(3m + 10) = 3(m + 5) + 15

Reorder the terms:
(2 + m)(3m + 10) = 3(m + 5) + 15

Reorder the terms:
(2 + m)(10 + 3m) = 3(m + 5) + 15

Multiply (2 + m) * (10 + 3m)
(2(10 + 3m) + m(10 + 3m)) = 3(m + 5) + 15
((10 * 2 + 3m * 2) + m(10 + 3m)) = 3(m + 5) + 15
((20 + 6m) + m(10 + 3m)) = 3(m + 5) + 15
(20 + 6m + (10 * m + 3m * m)) = 3(m + 5) + 15
(20 + 6m + (10m + 3m2)) = 3(m + 5) + 15

Combine like terms: 6m + 10m = 16m
(20 + 16m + 3m2) = 3(m + 5) + 15

Reorder the terms:
20 + 16m + 3m2 = 3(5 + m) + 15
20 + 16m + 3m2 = (5 * 3 + m * 3) + 15
20 + 16m + 3m2 = (15 + 3m) + 15

Reorder the terms:
20 + 16m + 3m2 = 15 + 15 + 3m

Combine like terms: 15 + 15 = 30
20 + 16m + 3m2 = 30 + 3m

Solving
20 + 16m + 3m2 = 30 + 3m

Solving for variable 'm'.

Reorder the terms:
20 + -30 + 16m + -3m + 3m2 = 30 + 3m + -30 + -3m

Combine like terms: 20 + -30 = -10
-10 + 16m + -3m + 3m2 = 30 + 3m + -30 + -3m

Combine like terms: 16m + -3m = 13m
-10 + 13m + 3m2 = 30 + 3m + -30 + -3m

Reorder the terms:
-10 + 13m + 3m2 = 30 + -30 + 3m + -3m

Combine like terms: 30 + -30 = 0
-10 + 13m + 3m2 = 0 + 3m + -3m
-10 + 13m + 3m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
-10 + 13m + 3m2 = 0

Factor a trinomial.
(-5 + -1m)(2 + -3m) = 0


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

Simplifying
-5 + -1m = 0

Solving
-5 + -1m = 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 + -1m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1m = 0 + 5
-1m = 0 + 5

Combine like terms: 0 + 5 = 5
-1m = 5

Divide each side by '-1'.
m = -5

Simplifying
m = -5

Subproblem 2
Set the factor '(2 + -3m)' equal to zero and attempt to solve:

Simplifying
2 + -3m = 0

Solving
2 + -3m = 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 + -3m = 0 + -2

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

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

Divide each side by '-3'.
m = 0.6666666667

Simplifying
m = 0.6666666667
Solution
m = {-5, 0.6666666667}

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