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Simplifying 3x(x + 5)(2x + -7)(3x + -13) = 0 Reorder the terms: 3x(5 + x)(2x + -7)(3x + -13) = 0 Reorder the terms: 3x(5 + x)(-7 + 2x)(3x + -13) = 0 Reorder the terms: 3x(5 + x)(-7 + 2x)(-13 + 3x) = 0 Multiply (5 + x) * (-7 + 2x) 3x(5(-7 + 2x) + x(-7 + 2x))(-13 + 3x) = 0 3x((-7 * 5 + 2x * 5) + x(-7 + 2x))(-13 + 3x) = 0 3x((-35 + 10x) + x(-7 + 2x))(-13 + 3x) = 0 3x(-35 + 10x + (-7 * x + 2x * x))(-13 + 3x) = 0 3x(-35 + 10x + (-7x + 2x2))(-13 + 3x) = 0 Combine like terms: 10x + -7x = 3x 3x(-35 + 3x + 2x2)(-13 + 3x) = 0 Multiply (-35 + 3x + 2x2) * (-13 + 3x) 3x(-35(-13 + 3x) + 3x * (-13 + 3x) + 2x2 * (-13 + 3x)) = 0 3x((-13 * -35 + 3x * -35) + 3x * (-13 + 3x) + 2x2 * (-13 + 3x)) = 0 3x((455 + -105x) + 3x * (-13 + 3x) + 2x2 * (-13 + 3x)) = 0 3x(455 + -105x + (-13 * 3x + 3x * 3x) + 2x2 * (-13 + 3x)) = 0 3x(455 + -105x + (-39x + 9x2) + 2x2 * (-13 + 3x)) = 0 3x(455 + -105x + -39x + 9x2 + (-13 * 2x2 + 3x * 2x2)) = 0 3x(455 + -105x + -39x + 9x2 + (-26x2 + 6x3)) = 0 Combine like terms: -105x + -39x = -144x 3x(455 + -144x + 9x2 + -26x2 + 6x3) = 0 Combine like terms: 9x2 + -26x2 = -17x2 3x(455 + -144x + -17x2 + 6x3) = 0 (455 * 3x + -144x * 3x + -17x2 * 3x + 6x3 * 3x) = 0 (1365x + -432x2 + -51x3 + 18x4) = 0 Solving 1365x + -432x2 + -51x3 + 18x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(455 + -144x + -17x2 + 6x3) = 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 '(455 + -144x + -17x2 + 6x3)' equal to zero and attempt to solve: Simplifying 455 + -144x + -17x2 + 6x3 = 0 Solving 455 + -144x + -17x2 + 6x3 = 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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