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Simplifying (4x2 + 3)(x + -4)(x + 4) = 0 Reorder the terms: (3 + 4x2)(x + -4)(x + 4) = 0 Reorder the terms: (3 + 4x2)(-4 + x)(x + 4) = 0 Reorder the terms: (3 + 4x2)(-4 + x)(4 + x) = 0 Multiply (3 + 4x2) * (-4 + x) (3(-4 + x) + 4x2 * (-4 + x))(4 + x) = 0 ((-4 * 3 + x * 3) + 4x2 * (-4 + x))(4 + x) = 0 ((-12 + 3x) + 4x2 * (-4 + x))(4 + x) = 0 (-12 + 3x + (-4 * 4x2 + x * 4x2))(4 + x) = 0 (-12 + 3x + (-16x2 + 4x3))(4 + x) = 0 (-12 + 3x + -16x2 + 4x3)(4 + x) = 0 Multiply (-12 + 3x + -16x2 + 4x3) * (4 + x) (-12(4 + x) + 3x * (4 + x) + -16x2 * (4 + x) + 4x3 * (4 + x)) = 0 ((4 * -12 + x * -12) + 3x * (4 + x) + -16x2 * (4 + x) + 4x3 * (4 + x)) = 0 ((-48 + -12x) + 3x * (4 + x) + -16x2 * (4 + x) + 4x3 * (4 + x)) = 0 (-48 + -12x + (4 * 3x + x * 3x) + -16x2 * (4 + x) + 4x3 * (4 + x)) = 0 (-48 + -12x + (12x + 3x2) + -16x2 * (4 + x) + 4x3 * (4 + x)) = 0 (-48 + -12x + 12x + 3x2 + (4 * -16x2 + x * -16x2) + 4x3 * (4 + x)) = 0 (-48 + -12x + 12x + 3x2 + (-64x2 + -16x3) + 4x3 * (4 + x)) = 0 (-48 + -12x + 12x + 3x2 + -64x2 + -16x3 + (4 * 4x3 + x * 4x3)) = 0 (-48 + -12x + 12x + 3x2 + -64x2 + -16x3 + (16x3 + 4x4)) = 0 Combine like terms: -12x + 12x = 0 (-48 + 0 + 3x2 + -64x2 + -16x3 + 16x3 + 4x4) = 0 (-48 + 3x2 + -64x2 + -16x3 + 16x3 + 4x4) = 0 Combine like terms: 3x2 + -64x2 = -61x2 (-48 + -61x2 + -16x3 + 16x3 + 4x4) = 0 Combine like terms: -16x3 + 16x3 = 0 (-48 + -61x2 + 0 + 4x4) = 0 (-48 + -61x2 + 4x4) = 0 Solving -48 + -61x2 + 4x4 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -4x2)(16 + -1x2) = 0 Factor a difference between two squares. (-3 + -4x2)((4 + x)(4 + -1x)) = 0Subproblem 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 '(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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