20a^2=16-32a

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Solution for 20a^2=16-32a equation:


Simplifying
20a2 = 16 + -32a

Solving
20a2 = 16 + -32a

Solving for variable 'a'.

Reorder the terms:
-16 + 32a + 20a2 = 16 + -32a + -16 + 32a

Reorder the terms:
-16 + 32a + 20a2 = 16 + -16 + -32a + 32a

Combine like terms: 16 + -16 = 0
-16 + 32a + 20a2 = 0 + -32a + 32a
-16 + 32a + 20a2 = -32a + 32a

Combine like terms: -32a + 32a = 0
-16 + 32a + 20a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 8a + 5a2) = 0

Factor a trinomial.
4((-2 + -1a)(2 + -5a)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2

Subproblem 2

Set the factor '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4

Solution

a = {-2, 0.4}

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