(m-2)(m-3)+(m-2)(m+4)=

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


Simplifying
(m + -2)(m + -3) + (m + -2)(m + 4) = 0

Reorder the terms:
(-2 + m)(m + -3) + (m + -2)(m + 4) = 0

Reorder the terms:
(-2 + m)(-3 + m) + (m + -2)(m + 4) = 0

Multiply (-2 + m) * (-3 + m)
(-2(-3 + m) + m(-3 + m)) + (m + -2)(m + 4) = 0
((-3 * -2 + m * -2) + m(-3 + m)) + (m + -2)(m + 4) = 0
((6 + -2m) + m(-3 + m)) + (m + -2)(m + 4) = 0
(6 + -2m + (-3 * m + m * m)) + (m + -2)(m + 4) = 0
(6 + -2m + (-3m + m2)) + (m + -2)(m + 4) = 0

Combine like terms: -2m + -3m = -5m
(6 + -5m + m2) + (m + -2)(m + 4) = 0

Reorder the terms:
6 + -5m + m2 + (-2 + m)(m + 4) = 0

Reorder the terms:
6 + -5m + m2 + (-2 + m)(4 + m) = 0

Multiply (-2 + m) * (4 + m)
6 + -5m + m2 + (-2(4 + m) + m(4 + m)) = 0
6 + -5m + m2 + ((4 * -2 + m * -2) + m(4 + m)) = 0
6 + -5m + m2 + ((-8 + -2m) + m(4 + m)) = 0
6 + -5m + m2 + (-8 + -2m + (4 * m + m * m)) = 0
6 + -5m + m2 + (-8 + -2m + (4m + m2)) = 0

Combine like terms: -2m + 4m = 2m
6 + -5m + m2 + (-8 + 2m + m2) = 0

Reorder the terms:
6 + -8 + -5m + 2m + m2 + m2 = 0

Combine like terms: 6 + -8 = -2
-2 + -5m + 2m + m2 + m2 = 0

Combine like terms: -5m + 2m = -3m
-2 + -3m + m2 + m2 = 0

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

Solving
-2 + -3m + 2m2 = 0

Solving for variable 'm'.

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

Subproblem 1

Set the factor '(-1 + -2m)' equal to zero and attempt to solve: Simplifying -1 + -2m = 0 Solving -1 + -2m = 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 + -2m = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2m = 0 + 1 -2m = 0 + 1 Combine like terms: 0 + 1 = 1 -2m = 1 Divide each side by '-2'. m = -0.5 Simplifying m = -0.5

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 = {-0.5, 2}

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