75(4x^2+3)(6x^2+1)=0

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Solution for 75(4x^2+3)(6x^2+1)=0 equation:


Simplifying
75(4x2 + 3)(6x2 + 1) = 0

Reorder the terms:
75(3 + 4x2)(6x2 + 1) = 0

Reorder the terms:
75(3 + 4x2)(1 + 6x2) = 0

Multiply (3 + 4x2) * (1 + 6x2)
75(3(1 + 6x2) + 4x2 * (1 + 6x2)) = 0
75((1 * 3 + 6x2 * 3) + 4x2 * (1 + 6x2)) = 0
75((3 + 18x2) + 4x2 * (1 + 6x2)) = 0
75(3 + 18x2 + (1 * 4x2 + 6x2 * 4x2)) = 0
75(3 + 18x2 + (4x2 + 24x4)) = 0

Combine like terms: 18x2 + 4x2 = 22x2
75(3 + 22x2 + 24x4) = 0
(3 * 75 + 22x2 * 75 + 24x4 * 75) = 0
(225 + 1650x2 + 1800x4) = 0

Solving
225 + 1650x2 + 1800x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '75'.
75(3 + 22x2 + 24x4) = 0

Factor a trinomial.
75((3 + 4x2)(1 + 6x2)) = 0

Ignore the factor 75.

Subproblem 1

Set the factor '(3 + 4x2)' equal to zero and attempt to solve: Simplifying 3 + 4x2 = 0 Solving 3 + 4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x2 = 0 + -3 4x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4x2 = -3 Divide each side by '4'. x2 = -0.75 Simplifying x2 = -0.75 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + 6x2)' equal to zero and attempt to solve: Simplifying 1 + 6x2 = 0 Solving 1 + 6x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x2 = 0 + -1 6x2 = 0 + -1 Combine like terms: 0 + -1 = -1 6x2 = -1 Divide each side by '6'. x2 = -0.1666666667 Simplifying x2 = -0.1666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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