a^2-4=-4a^2-8a

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Solution for a^2-4=-4a^2-8a equation:


Simplifying
a2 + -4 = -4a2 + -8a

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

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

Solving
-4 + a2 = -8a + -4a2

Solving for variable 'a'.

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

Combine like terms: a2 + 4a2 = 5a2
-4 + 8a + 5a2 = -8a + -4a2 + 8a + 4a2

Reorder the terms:
-4 + 8a + 5a2 = -8a + 8a + -4a2 + 4a2

Combine like terms: -8a + 8a = 0
-4 + 8a + 5a2 = 0 + -4a2 + 4a2
-4 + 8a + 5a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
-4 + 8a + 5a2 = 0

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

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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