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Simplifying (7 + -3x)(2x + -6) = -42 Reorder the terms: (7 + -3x)(-6 + 2x) = -42 Multiply (7 + -3x) * (-6 + 2x) (7(-6 + 2x) + -3x * (-6 + 2x)) = -42 ((-6 * 7 + 2x * 7) + -3x * (-6 + 2x)) = -42 ((-42 + 14x) + -3x * (-6 + 2x)) = -42 (-42 + 14x + (-6 * -3x + 2x * -3x)) = -42 (-42 + 14x + (18x + -6x2)) = -42 Combine like terms: 14x + 18x = 32x (-42 + 32x + -6x2) = -42 Add '42' to each side of the equation. -42 + 32x + 42 + -6x2 = -42 + 42 Reorder the terms: -42 + 42 + 32x + -6x2 = -42 + 42 Combine like terms: -42 + 42 = 0 0 + 32x + -6x2 = -42 + 42 32x + -6x2 = -42 + 42 Combine like terms: -42 + 42 = 0 32x + -6x2 = 0 Solving 32x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(16 + -3x) = 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 '(16 + -3x)' equal to zero and attempt to solve: Simplifying 16 + -3x = 0 Solving 16 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -3x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -3x = 0 + -16 -3x = 0 + -16 Combine like terms: 0 + -16 = -16 -3x = -16 Divide each side by '-3'. x = 5.333333333 Simplifying x = 5.333333333Solution
x = {0, 5.333333333}
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