(m-5)(m+2)=18

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Solution for (m-5)(m+2)=18 equation: 


Simplifying
(m + -5)(m + 2) = 18

Reorder the terms:
(-5 + m)(m + 2) = 18

Reorder the terms:
(-5 + m)(2 + m) = 18

Multiply (-5 + m) * (2 + m)
(-5(2 + m) + m(2 + m)) = 18
((2 * -5 + m * -5) + m(2 + m)) = 18
((-10 + -5m) + m(2 + m)) = 18
(-10 + -5m + (2 * m + m * m)) = 18
(-10 + -5m + (2m + m2)) = 18

Combine like terms: -5m + 2m = -3m
(-10 + -3m + m2) = 18

Solving
-10 + -3m + m2 = 18

Solving for variable 'm'.

Reorder the terms:
-10 + -18 + -3m + m2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + -3m + m2 = 18 + -18

Combine like terms: 18 + -18 = 0
-28 + -3m + m2 = 0

Factor a trinomial.
(-4 + -1m)(7 + -1m) = 0


Subproblem 1
Set the factor '(-4 + -1m)' equal to zero and attempt to solve:

Simplifying
-4 + -1m = 0

Solving
-4 + -1m = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1m = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1m = 0 + 4
-1m = 0 + 4

Combine like terms: 0 + 4 = 4
-1m = 4

Divide each side by '-1'.
m = -4

Simplifying
m = -4

Subproblem 2
Set the factor '(7 + -1m)' equal to zero and attempt to solve:

Simplifying
7 + -1m = 0

Solving
7 + -1m = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1m = 0 + -7
-1m = 0 + -7

Combine like terms: 0 + -7 = -7
-1m = -7

Divide each side by '-1'.
m = 7

Simplifying
m = 7
Solution
m = {-4, 7}

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