(-10x^4-12x^2)(3x^2-5)=

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Solution for (-10x^4-12x^2)(3x^2-5)= equation:


Simplifying
(-10x4 + -12x2)(3x2 + -5) = 0

Reorder the terms:
(-12x2 + -10x4)(3x2 + -5) = 0

Reorder the terms:
(-12x2 + -10x4)(-5 + 3x2) = 0

Multiply (-12x2 + -10x4) * (-5 + 3x2)
(-12x2 * (-5 + 3x2) + -10x4 * (-5 + 3x2)) = 0
((-5 * -12x2 + 3x2 * -12x2) + -10x4 * (-5 + 3x2)) = 0
((60x2 + -36x4) + -10x4 * (-5 + 3x2)) = 0
(60x2 + -36x4 + (-5 * -10x4 + 3x2 * -10x4)) = 0
(60x2 + -36x4 + (50x4 + -30x6)) = 0

Combine like terms: -36x4 + 50x4 = 14x4
(60x2 + 14x4 + -30x6) = 0

Solving
60x2 + 14x4 + -30x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(30 + 7x2 + -15x4) = 0

Factor a trinomial.
2x2((5 + -3x2)(6 + 5x2)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(5 + -3x2)' equal to zero and attempt to solve: Simplifying 5 + -3x2 = 0 Solving 5 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x2 = 0 + -5 -3x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3x2 = -5 Divide each side by '-3'. x2 = 1.666666667 Simplifying x2 = 1.666666667 Take the square root of each side: x = {-1.290994449, 1.290994449}

Subproblem 3

Set the factor '(6 + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 5x2 = 0 Solving 6 + 5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x2 = 0 + -6 5x2 = 0 + -6 Combine like terms: 0 + -6 = -6 5x2 = -6 Divide each side by '5'. x2 = -1.2 Simplifying x2 = -1.2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0, -1.290994449, 1.290994449}

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