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Simplifying 48xy2(5x + -7)(3x + 4) + -32y2x(4 + 3x)(3x + -4) = 0 Reorder the terms: 48xy2(-7 + 5x)(3x + 4) + -32y2x(4 + 3x)(3x + -4) = 0 Reorder the terms: 48xy2(-7 + 5x)(4 + 3x) + -32y2x(4 + 3x)(3x + -4) = 0 Multiply (-7 + 5x) * (4 + 3x) 48xy2(-7(4 + 3x) + 5x * (4 + 3x)) + -32y2x(4 + 3x)(3x + -4) = 0 48xy2((4 * -7 + 3x * -7) + 5x * (4 + 3x)) + -32y2x(4 + 3x)(3x + -4) = 0 48xy2((-28 + -21x) + 5x * (4 + 3x)) + -32y2x(4 + 3x)(3x + -4) = 0 48xy2(-28 + -21x + (4 * 5x + 3x * 5x)) + -32y2x(4 + 3x)(3x + -4) = 0 48xy2(-28 + -21x + (20x + 15x2)) + -32y2x(4 + 3x)(3x + -4) = 0 Combine like terms: -21x + 20x = -1x 48xy2(-28 + -1x + 15x2) + -32y2x(4 + 3x)(3x + -4) = 0 (-28 * 48xy2 + -1x * 48xy2 + 15x2 * 48xy2) + -32y2x(4 + 3x)(3x + -4) = 0 (-1344xy2 + -48x2y2 + 720x3y2) + -32y2x(4 + 3x)(3x + -4) = 0 Reorder the terms: -1344xy2 + -48x2y2 + 720x3y2 + -32xy2(4 + 3x)(-4 + 3x) = 0 Multiply (4 + 3x) * (-4 + 3x) -1344xy2 + -48x2y2 + 720x3y2 + -32xy2(4(-4 + 3x) + 3x * (-4 + 3x)) = 0 -1344xy2 + -48x2y2 + 720x3y2 + -32xy2((-4 * 4 + 3x * 4) + 3x * (-4 + 3x)) = 0 -1344xy2 + -48x2y2 + 720x3y2 + -32xy2((-16 + 12x) + 3x * (-4 + 3x)) = 0 -1344xy2 + -48x2y2 + 720x3y2 + -32xy2(-16 + 12x + (-4 * 3x + 3x * 3x)) = 0 -1344xy2 + -48x2y2 + 720x3y2 + -32xy2(-16 + 12x + (-12x + 9x2)) = 0 Combine like terms: 12x + -12x = 0 -1344xy2 + -48x2y2 + 720x3y2 + -32xy2(-16 + 0 + 9x2) = 0 -1344xy2 + -48x2y2 + 720x3y2 + -32xy2(-16 + 9x2) = 0 -1344xy2 + -48x2y2 + 720x3y2 + (-16 * -32xy2 + 9x2 * -32xy2) = 0 -1344xy2 + -48x2y2 + 720x3y2 + (512xy2 + -288x3y2) = 0 Reorder the terms: -1344xy2 + 512xy2 + -48x2y2 + 720x3y2 + -288x3y2 = 0 Combine like terms: -1344xy2 + 512xy2 = -832xy2 -832xy2 + -48x2y2 + 720x3y2 + -288x3y2 = 0 Combine like terms: 720x3y2 + -288x3y2 = 432x3y2 -832xy2 + -48x2y2 + 432x3y2 = 0 Solving -832xy2 + -48x2y2 + 432x3y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16xy2'. 16xy2(-52 + -3x + 27x2) = 0 Factor a trinomial. 16xy2((-4 + -3x)(13 + -9x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve: Simplifying xy2 = 0 Solving xy2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy2 = 0 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 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 3
Set the factor '(13 + -9x)' equal to zero and attempt to solve: Simplifying 13 + -9x = 0 Solving 13 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -9x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -9x = 0 + -13 -9x = 0 + -13 Combine like terms: 0 + -13 = -13 -9x = -13 Divide each side by '-9'. x = 1.444444444 Simplifying x = 1.444444444Solution
x = {-1.333333333, 1.444444444}
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