(4m+7)(m-2)=-2m(5m+9)-17

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Solution for (4m+7)(m-2)=-2m(5m+9)-17 equation: 


Simplifying
(4m + 7)(m + -2) = -2m(5m + 9) + -17

Reorder the terms:
(7 + 4m)(m + -2) = -2m(5m + 9) + -17

Reorder the terms:
(7 + 4m)(-2 + m) = -2m(5m + 9) + -17

Multiply (7 + 4m) * (-2 + m)
(7(-2 + m) + 4m * (-2 + m)) = -2m(5m + 9) + -17
((-2 * 7 + m * 7) + 4m * (-2 + m)) = -2m(5m + 9) + -17
((-14 + 7m) + 4m * (-2 + m)) = -2m(5m + 9) + -17
(-14 + 7m + (-2 * 4m + m * 4m)) = -2m(5m + 9) + -17
(-14 + 7m + (-8m + 4m2)) = -2m(5m + 9) + -17

Combine like terms: 7m + -8m = -1m
(-14 + -1m + 4m2) = -2m(5m + 9) + -17

Reorder the terms:
-14 + -1m + 4m2 = -2m(9 + 5m) + -17
-14 + -1m + 4m2 = (9 * -2m + 5m * -2m) + -17
-14 + -1m + 4m2 = (-18m + -10m2) + -17

Reorder the terms:
-14 + -1m + 4m2 = -17 + -18m + -10m2

Solving
-14 + -1m + 4m2 = -17 + -18m + -10m2

Solving for variable 'm'.

Reorder the terms:
-14 + 17 + -1m + 18m + 4m2 + 10m2 = -17 + -18m + -10m2 + 17 + 18m + 10m2

Combine like terms: -14 + 17 = 3
3 + -1m + 18m + 4m2 + 10m2 = -17 + -18m + -10m2 + 17 + 18m + 10m2

Combine like terms: -1m + 18m = 17m
3 + 17m + 4m2 + 10m2 = -17 + -18m + -10m2 + 17 + 18m + 10m2

Combine like terms: 4m2 + 10m2 = 14m2
3 + 17m + 14m2 = -17 + -18m + -10m2 + 17 + 18m + 10m2

Reorder the terms:
3 + 17m + 14m2 = -17 + 17 + -18m + 18m + -10m2 + 10m2

Combine like terms: -17 + 17 = 0
3 + 17m + 14m2 = 0 + -18m + 18m + -10m2 + 10m2
3 + 17m + 14m2 = -18m + 18m + -10m2 + 10m2

Combine like terms: -18m + 18m = 0
3 + 17m + 14m2 = 0 + -10m2 + 10m2
3 + 17m + 14m2 = -10m2 + 10m2

Combine like terms: -10m2 + 10m2 = 0
3 + 17m + 14m2 = 0

Factor a trinomial.
(1 + m)(3 + 14m) = 0


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

Simplifying
1 + m = 0

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

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

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

Simplifying
m = -1

Subproblem 2
Set the factor '(3 + 14m)' equal to zero and attempt to solve:

Simplifying
3 + 14m = 0

Solving
3 + 14m = 0

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

Add '-3' to each side of the equation.
3 + -3 + 14m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 14m = 0 + -3
14m = 0 + -3

Combine like terms: 0 + -3 = -3
14m = -3

Divide each side by '14'.
m = -0.2142857143

Simplifying
m = -0.2142857143
Solution
m = {-1, -0.2142857143}

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