(m^2-4m+7)-(4m^2-4)-(-2m+6)=

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Solution for (m^2-4m+7)-(4m^2-4)-(-2m+6)= equation:


Simplifying
(m2 + -4m + 7) + -1(4m2 + -4) + -1(-2m + 6) = 0

Reorder the terms:
(7 + -4m + m2) + -1(4m2 + -4) + -1(-2m + 6) = 0

Remove parenthesis around (7 + -4m + m2)
7 + -4m + m2 + -1(4m2 + -4) + -1(-2m + 6) = 0

Reorder the terms:
7 + -4m + m2 + -1(-4 + 4m2) + -1(-2m + 6) = 0
7 + -4m + m2 + (-4 * -1 + 4m2 * -1) + -1(-2m + 6) = 0
7 + -4m + m2 + (4 + -4m2) + -1(-2m + 6) = 0

Reorder the terms:
7 + -4m + m2 + 4 + -4m2 + -1(6 + -2m) = 0
7 + -4m + m2 + 4 + -4m2 + (6 * -1 + -2m * -1) = 0
7 + -4m + m2 + 4 + -4m2 + (-6 + 2m) = 0

Reorder the terms:
7 + 4 + -6 + -4m + 2m + m2 + -4m2 = 0

Combine like terms: 7 + 4 = 11
11 + -6 + -4m + 2m + m2 + -4m2 = 0

Combine like terms: 11 + -6 = 5
5 + -4m + 2m + m2 + -4m2 = 0

Combine like terms: -4m + 2m = -2m
5 + -2m + m2 + -4m2 = 0

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

Solving
5 + -2m + -3m2 = 0

Solving for variable 'm'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(5 + 3m)' equal to zero and attempt to solve: Simplifying 5 + 3m = 0 Solving 5 + 3m = 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 + 3m = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3m = 0 + -5 3m = 0 + -5 Combine like terms: 0 + -5 = -5 3m = -5 Divide each side by '3'. m = -1.666666667 Simplifying m = -1.666666667

Solution

m = {1, -1.666666667}

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