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Simplifying 3x(2x + x2) + 5x(3x + -4x2) = 0 (2x * 3x + x2 * 3x) + 5x(3x + -4x2) = 0 (6x2 + 3x3) + 5x(3x + -4x2) = 0 6x2 + 3x3 + (3x * 5x + -4x2 * 5x) = 0 6x2 + 3x3 + (15x2 + -20x3) = 0 Reorder the terms: 6x2 + 15x2 + 3x3 + -20x3 = 0 Combine like terms: 6x2 + 15x2 = 21x2 21x2 + 3x3 + -20x3 = 0 Combine like terms: 3x3 + -20x3 = -17x3 21x2 + -17x3 = 0 Solving 21x2 + -17x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(21 + -17x) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(21 + -17x)' equal to zero and attempt to solve: Simplifying 21 + -17x = 0 Solving 21 + -17x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -17x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -17x = 0 + -21 -17x = 0 + -21 Combine like terms: 0 + -21 = -21 -17x = -21 Divide each side by '-17'. x = 1.235294118 Simplifying x = 1.235294118Solution
x = {0, 1.235294118}
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