(7-2m)(2m+7)-49=m(m-2)

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Solution for (7-2m)(2m+7)-49=m(m-2) equation: 


Simplifying
(7 + -2m)(2m + 7) + -49 = m(m + -2)

Reorder the terms:
(7 + -2m)(7 + 2m) + -49 = m(m + -2)

Multiply (7 + -2m) * (7 + 2m)
(7(7 + 2m) + -2m * (7 + 2m)) + -49 = m(m + -2)
((7 * 7 + 2m * 7) + -2m * (7 + 2m)) + -49 = m(m + -2)
((49 + 14m) + -2m * (7 + 2m)) + -49 = m(m + -2)
(49 + 14m + (7 * -2m + 2m * -2m)) + -49 = m(m + -2)
(49 + 14m + (-14m + -4m2)) + -49 = m(m + -2)

Combine like terms: 14m + -14m = 0
(49 + 0 + -4m2) + -49 = m(m + -2)
(49 + -4m2) + -49 = m(m + -2)

Reorder the terms:
49 + -49 + -4m2 = m(m + -2)

Combine like terms: 49 + -49 = 0
0 + -4m2 = m(m + -2)
-4m2 = m(m + -2)

Reorder the terms:
-4m2 = m(-2 + m)
-4m2 = (-2 * m + m * m)
-4m2 = (-2m + m2)

Solving
-4m2 = -2m + m2

Solving for variable 'm'.

Reorder the terms:
2m + -4m2 + -1m2 = -2m + m2 + 2m + -1m2

Combine like terms: -4m2 + -1m2 = -5m2
2m + -5m2 = -2m + m2 + 2m + -1m2

Reorder the terms:
2m + -5m2 = -2m + 2m + m2 + -1m2

Combine like terms: -2m + 2m = 0
2m + -5m2 = 0 + m2 + -1m2
2m + -5m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
2m + -5m2 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(2 + -5m) = 0


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

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0

Subproblem 2
Set the factor '(2 + -5m)' equal to zero and attempt to solve:

Simplifying
2 + -5m = 0

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

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

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

Divide each side by '-5'.
m = 0.4

Simplifying
m = 0.4
Solution
m = {0, 0.4}

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