4a-2a^2=6-4a

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Solution for 4a-2a^2=6-4a equation:


Simplifying
4a + -2a2 = 6 + -4a

Solving
4a + -2a2 = 6 + -4a

Solving for variable 'a'.

Reorder the terms:
-6 + 4a + 4a + -2a2 = 6 + -4a + -6 + 4a

Combine like terms: 4a + 4a = 8a
-6 + 8a + -2a2 = 6 + -4a + -6 + 4a

Reorder the terms:
-6 + 8a + -2a2 = 6 + -6 + -4a + 4a

Combine like terms: 6 + -6 = 0
-6 + 8a + -2a2 = 0 + -4a + 4a
-6 + 8a + -2a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
-6 + 8a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4a + -1a2) = 0

Factor a trinomial.
2((-3 + a)(1 + -1a)) = 0

Ignore the factor 2.

Subproblem 1

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

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 = {3, 1}

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