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Simplifying (5x3 + -10x2 + 7x) + -1(5x3 + 6x2 + x) = 0 Reorder the terms: (7x + -10x2 + 5x3) + -1(5x3 + 6x2 + x) = 0 Remove parenthesis around (7x + -10x2 + 5x3) 7x + -10x2 + 5x3 + -1(5x3 + 6x2 + x) = 0 Reorder the terms: 7x + -10x2 + 5x3 + -1(x + 6x2 + 5x3) = 0 7x + -10x2 + 5x3 + (x * -1 + 6x2 * -1 + 5x3 * -1) = 0 7x + -10x2 + 5x3 + (-1x + -6x2 + -5x3) = 0 Reorder the terms: 7x + -1x + -10x2 + -6x2 + 5x3 + -5x3 = 0 Combine like terms: 7x + -1x = 6x 6x + -10x2 + -6x2 + 5x3 + -5x3 = 0 Combine like terms: -10x2 + -6x2 = -16x2 6x + -16x2 + 5x3 + -5x3 = 0 Combine like terms: 5x3 + -5x3 = 0 6x + -16x2 + 0 = 0 6x + -16x2 = 0 Solving 6x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -8x) = 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 '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375Solution
x = {0, 0.375}
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