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Simplifying 6(2x2 + 4x) + 10(4x2 + 3x) = 0 Reorder the terms: 6(4x + 2x2) + 10(4x2 + 3x) = 0 (4x * 6 + 2x2 * 6) + 10(4x2 + 3x) = 0 (24x + 12x2) + 10(4x2 + 3x) = 0 Reorder the terms: 24x + 12x2 + 10(3x + 4x2) = 0 24x + 12x2 + (3x * 10 + 4x2 * 10) = 0 24x + 12x2 + (30x + 40x2) = 0 Reorder the terms: 24x + 30x + 12x2 + 40x2 = 0 Combine like terms: 24x + 30x = 54x 54x + 12x2 + 40x2 = 0 Combine like terms: 12x2 + 40x2 = 52x2 54x + 52x2 = 0 Solving 54x + 52x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(27 + 26x) = 0 Ignore the factor 2.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 '(27 + 26x)' equal to zero and attempt to solve: Simplifying 27 + 26x = 0 Solving 27 + 26x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 26x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 26x = 0 + -27 26x = 0 + -27 Combine like terms: 0 + -27 = -27 26x = -27 Divide each side by '26'. x = -1.038461538 Simplifying x = -1.038461538Solution
x = {0, -1.038461538}
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