21a^2-49=-28a

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Solution for 21a^2-49=-28a equation:


Simplifying
21a2 + -49 = -28a

Reorder the terms:
-49 + 21a2 = -28a

Solving
-49 + 21a2 = -28a

Solving for variable 'a'.

Reorder the terms:
-49 + 28a + 21a2 = -28a + 28a

Combine like terms: -28a + 28a = 0
-49 + 28a + 21a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + 4a + 3a2) = 0

Factor a trinomial.
7((-7 + -3a)(1 + -1a)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-7 + -3a)' equal to zero and attempt to solve: Simplifying -7 + -3a = 0 Solving -7 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3a = 0 + 7 -3a = 0 + 7 Combine like terms: 0 + 7 = 7 -3a = 7 Divide each side by '-3'. a = -2.333333333 Simplifying a = -2.333333333

Subproblem 2

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

Solution

a = {-2.333333333, 1}

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