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Simplifying (5x2 + 20)(3x2 + -48) = 0 Reorder the terms: (20 + 5x2)(3x2 + -48) = 0 Reorder the terms: (20 + 5x2)(-48 + 3x2) = 0 Multiply (20 + 5x2) * (-48 + 3x2) (20(-48 + 3x2) + 5x2 * (-48 + 3x2)) = 0 ((-48 * 20 + 3x2 * 20) + 5x2 * (-48 + 3x2)) = 0 ((-960 + 60x2) + 5x2 * (-48 + 3x2)) = 0 (-960 + 60x2 + (-48 * 5x2 + 3x2 * 5x2)) = 0 (-960 + 60x2 + (-240x2 + 15x4)) = 0 Combine like terms: 60x2 + -240x2 = -180x2 (-960 + -180x2 + 15x4) = 0 Solving -960 + -180x2 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(-64 + -12x2 + x4) = 0 Factor a trinomial. 15((-4 + -1x2)(16 + -1x2)) = 0 Factor a difference between two squares. 15((-4 + -1x2)((4 + x)(4 + -1x))) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve: Simplifying -4 + -1x2 = 0 Solving -4 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x2 = 0 + 4 -1x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x2 = 4 Divide each side by '-1'. x2 = -4 Simplifying x2 = -4 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4, 4}
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