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Simplifying 15x3 = 17x2 + 42x Reorder the terms: 15x3 = 42x + 17x2 Solving 15x3 = 42x + 17x2 Solving for variable 'x'. Reorder the terms: -42x + -17x2 + 15x3 = 42x + 17x2 + -42x + -17x2 Reorder the terms: -42x + -17x2 + 15x3 = 42x + -42x + 17x2 + -17x2 Combine like terms: 42x + -42x = 0 -42x + -17x2 + 15x3 = 0 + 17x2 + -17x2 -42x + -17x2 + 15x3 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 -42x + -17x2 + 15x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-42 + -17x + 15x2) = 0 Factor a trinomial. x((-6 + -5x)(7 + -3x)) = 0Subproblem 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 '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2Subproblem 3
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {0, -1.2, 2.333333333}
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