10m^2-30=-55m

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Solution for 10m^2-30=-55m equation:


Simplifying
10m2 + -30 = -55m

Reorder the terms:
-30 + 10m2 = -55m

Solving
-30 + 10m2 = -55m

Solving for variable 'm'.

Reorder the terms:
-30 + 55m + 10m2 = -55m + 55m

Combine like terms: -55m + 55m = 0
-30 + 55m + 10m2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 11m + 2m2) = 0

Factor a trinomial.
5((-6 + -1m)(1 + -2m)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-6 + -1m)' equal to zero and attempt to solve: Simplifying -6 + -1m = 0 Solving -6 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1m = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1m = 0 + 6 -1m = 0 + 6 Combine like terms: 0 + 6 = 6 -1m = 6 Divide each side by '-1'. m = -6 Simplifying m = -6

Subproblem 2

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

Solution

m = {-6, 0.5}

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