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Simplifying 3x(x + 5)(2x + -7)(3x + 4)(x + -13) = 0 Reorder the terms: 3x(5 + x)(2x + -7)(3x + 4)(x + -13) = 0 Reorder the terms: 3x(5 + x)(-7 + 2x)(3x + 4)(x + -13) = 0 Reorder the terms: 3x(5 + x)(-7 + 2x)(4 + 3x)(x + -13) = 0 Reorder the terms: 3x(5 + x)(-7 + 2x)(4 + 3x)(-13 + x) = 0 Multiply (5 + x) * (-7 + 2x) 3x(5(-7 + 2x) + x(-7 + 2x))(4 + 3x)(-13 + x) = 0 3x((-7 * 5 + 2x * 5) + x(-7 + 2x))(4 + 3x)(-13 + x) = 0 3x((-35 + 10x) + x(-7 + 2x))(4 + 3x)(-13 + x) = 0 3x(-35 + 10x + (-7 * x + 2x * x))(4 + 3x)(-13 + x) = 0 3x(-35 + 10x + (-7x + 2x2))(4 + 3x)(-13 + x) = 0 Combine like terms: 10x + -7x = 3x 3x(-35 + 3x + 2x2)(4 + 3x)(-13 + x) = 0 Multiply (-35 + 3x + 2x2) * (4 + 3x) 3x(-35(4 + 3x) + 3x * (4 + 3x) + 2x2 * (4 + 3x))(-13 + x) = 0 3x((4 * -35 + 3x * -35) + 3x * (4 + 3x) + 2x2 * (4 + 3x))(-13 + x) = 0 3x((-140 + -105x) + 3x * (4 + 3x) + 2x2 * (4 + 3x))(-13 + x) = 0 3x(-140 + -105x + (4 * 3x + 3x * 3x) + 2x2 * (4 + 3x))(-13 + x) = 0 3x(-140 + -105x + (12x + 9x2) + 2x2 * (4 + 3x))(-13 + x) = 0 3x(-140 + -105x + 12x + 9x2 + (4 * 2x2 + 3x * 2x2))(-13 + x) = 0 3x(-140 + -105x + 12x + 9x2 + (8x2 + 6x3))(-13 + x) = 0 Combine like terms: -105x + 12x = -93x 3x(-140 + -93x + 9x2 + 8x2 + 6x3)(-13 + x) = 0 Combine like terms: 9x2 + 8x2 = 17x2 3x(-140 + -93x + 17x2 + 6x3)(-13 + x) = 0 Multiply (-140 + -93x + 17x2 + 6x3) * (-13 + x) 3x(-140(-13 + x) + -93x * (-13 + x) + 17x2 * (-13 + x) + 6x3 * (-13 + x)) = 0 3x((-13 * -140 + x * -140) + -93x * (-13 + x) + 17x2 * (-13 + x) + 6x3 * (-13 + x)) = 0 3x((1820 + -140x) + -93x * (-13 + x) + 17x2 * (-13 + x) + 6x3 * (-13 + x)) = 0 3x(1820 + -140x + (-13 * -93x + x * -93x) + 17x2 * (-13 + x) + 6x3 * (-13 + x)) = 0 3x(1820 + -140x + (1209x + -93x2) + 17x2 * (-13 + x) + 6x3 * (-13 + x)) = 0 3x(1820 + -140x + 1209x + -93x2 + (-13 * 17x2 + x * 17x2) + 6x3 * (-13 + x)) = 0 3x(1820 + -140x + 1209x + -93x2 + (-221x2 + 17x3) + 6x3 * (-13 + x)) = 0 3x(1820 + -140x + 1209x + -93x2 + -221x2 + 17x3 + (-13 * 6x3 + x * 6x3)) = 0 3x(1820 + -140x + 1209x + -93x2 + -221x2 + 17x3 + (-78x3 + 6x4)) = 0 Combine like terms: -140x + 1209x = 1069x 3x(1820 + 1069x + -93x2 + -221x2 + 17x3 + -78x3 + 6x4) = 0 Combine like terms: -93x2 + -221x2 = -314x2 3x(1820 + 1069x + -314x2 + 17x3 + -78x3 + 6x4) = 0 Combine like terms: 17x3 + -78x3 = -61x3 3x(1820 + 1069x + -314x2 + -61x3 + 6x4) = 0 (1820 * 3x + 1069x * 3x + -314x2 * 3x + -61x3 * 3x + 6x4 * 3x) = 0 (5460x + 3207x2 + -942x3 + -183x4 + 18x5) = 0 Solving 5460x + 3207x2 + -942x3 + -183x4 + 18x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(1820 + 1069x + -314x2 + -61x3 + 6x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1820 + 1069x + -314x2 + -61x3 + 6x4)' equal to zero and attempt to solve: Simplifying 1820 + 1069x + -314x2 + -61x3 + 6x4 = 0 Solving 1820 + 1069x + -314x2 + -61x3 + 6x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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