(x^2-sa)(4x^2+3sa)=0

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Solution for (x^2-sa)(4x^2+3sa)=0 equation:


Simplifying
(x2 + -1sa)(4x2 + 3sa) = 0

Reorder the terms:
(-1as + x2)(4x2 + 3sa) = 0

Reorder the terms:
(-1as + x2)(3as + 4x2) = 0

Multiply (-1as + x2) * (3as + 4x2)
(-1as * (3as + 4x2) + x2(3as + 4x2)) = 0
((3as * -1as + 4x2 * -1as) + x2(3as + 4x2)) = 0

Reorder the terms:
((-4asx2 + -3a2s2) + x2(3as + 4x2)) = 0
((-4asx2 + -3a2s2) + x2(3as + 4x2)) = 0
(-4asx2 + -3a2s2 + (3as * x2 + 4x2 * x2)) = 0
(-4asx2 + -3a2s2 + (3asx2 + 4x4)) = 0

Reorder the terms:
(-4asx2 + 3asx2 + -3a2s2 + 4x4) = 0

Combine like terms: -4asx2 + 3asx2 = -1asx2
(-1asx2 + -3a2s2 + 4x4) = 0

Solving
-1asx2 + -3a2s2 + 4x4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3as + -4x2)(as + -1x2) = 0

Subproblem 1

Set the factor '(-3as + -4x2)' equal to zero and attempt to solve: Simplifying -3as + -4x2 = 0 Solving -3as + -4x2 = 0 Move all terms containing a to the left, all other terms to the right. Add '4x2' to each side of the equation. -3as + -4x2 + 4x2 = 0 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -3as + 0 = 0 + 4x2 -3as = 0 + 4x2 Remove the zero: -3as = 4x2 Divide each side by '-3s'. a = -1.333333333s-1x2 Simplifying a = -1.333333333s-1x2

Subproblem 2

Set the factor '(as + -1x2)' equal to zero and attempt to solve: Simplifying as + -1x2 = 0 Solving as + -1x2 = 0 Move all terms containing a to the left, all other terms to the right. Add 'x2' to each side of the equation. as + -1x2 + x2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 as + 0 = 0 + x2 as = 0 + x2 Remove the zero: as = x2 Divide each side by 's'. a = s-1x2 Simplifying a = s-1x2

Solution

a = {-1.333333333s-1x2, s-1x2}

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