21ab+3a-6ab-5abc-20ab+10a=25a

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Solution for 21ab+3a-6ab-5abc-20ab+10a=25a equation:


Simplifying
21ab + 3a + -6ab + -5abc + -20ab + 10a = 25a

Reorder the terms:
3a + 10a + 21ab + -6ab + -20ab + -5abc = 25a

Combine like terms: 3a + 10a = 13a
13a + 21ab + -6ab + -20ab + -5abc = 25a

Combine like terms: 21ab + -6ab = 15ab
13a + 15ab + -20ab + -5abc = 25a

Combine like terms: 15ab + -20ab = -5ab
13a + -5ab + -5abc = 25a

Solving
13a + -5ab + -5abc = 25a

Solving for variable 'a'.

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

Add '-25a' to each side of the equation.
13a + -5ab + -25a + -5abc = 25a + -25a

Reorder the terms:
13a + -25a + -5ab + -5abc = 25a + -25a

Combine like terms: 13a + -25a = -12a
-12a + -5ab + -5abc = 25a + -25a

Combine like terms: 25a + -25a = 0
-12a + -5ab + -5abc = 0

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(12 + 5b + 5bc) = 0

Ignore the factor -1.

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(12 + 5b + 5bc)' equal to zero and attempt to solve: Simplifying 12 + 5b + 5bc = 0 Solving 12 + 5b + 5bc = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 5b + -12 + 5bc = 0 + -12 Reorder the terms: 12 + -12 + 5b + 5bc = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5b + 5bc = 0 + -12 5b + 5bc = 0 + -12 Combine like terms: 0 + -12 = -12 5b + 5bc = -12 Add '-5b' to each side of the equation. 5b + -5b + 5bc = -12 + -5b Combine like terms: 5b + -5b = 0 0 + 5bc = -12 + -5b 5bc = -12 + -5b Add '-5bc' to each side of the equation. 5bc + -5bc = -12 + -5b + -5bc Combine like terms: 5bc + -5bc = 0 0 = -12 + -5b + -5bc Simplifying 0 = -12 + -5b + -5bc The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

a = {0}

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