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Simplifying (x + -2)(7 + -3x) + -1(4 + -1x)(7 + -3x) = -42 Reorder the terms: (-2 + x)(7 + -3x) + -1(4 + -1x)(7 + -3x) = -42 Multiply (-2 + x) * (7 + -3x) (-2(7 + -3x) + x(7 + -3x)) + -1(4 + -1x)(7 + -3x) = -42 ((7 * -2 + -3x * -2) + x(7 + -3x)) + -1(4 + -1x)(7 + -3x) = -42 ((-14 + 6x) + x(7 + -3x)) + -1(4 + -1x)(7 + -3x) = -42 (-14 + 6x + (7 * x + -3x * x)) + -1(4 + -1x)(7 + -3x) = -42 (-14 + 6x + (7x + -3x2)) + -1(4 + -1x)(7 + -3x) = -42 Combine like terms: 6x + 7x = 13x (-14 + 13x + -3x2) + -1(4 + -1x)(7 + -3x) = -42 Multiply (4 + -1x) * (7 + -3x) -14 + 13x + -3x2 + -1(4(7 + -3x) + -1x * (7 + -3x)) = -42 -14 + 13x + -3x2 + -1((7 * 4 + -3x * 4) + -1x * (7 + -3x)) = -42 -14 + 13x + -3x2 + -1((28 + -12x) + -1x * (7 + -3x)) = -42 -14 + 13x + -3x2 + -1(28 + -12x + (7 * -1x + -3x * -1x)) = -42 -14 + 13x + -3x2 + -1(28 + -12x + (-7x + 3x2)) = -42 Combine like terms: -12x + -7x = -19x -14 + 13x + -3x2 + -1(28 + -19x + 3x2) = -42 -14 + 13x + -3x2 + (28 * -1 + -19x * -1 + 3x2 * -1) = -42 -14 + 13x + -3x2 + (-28 + 19x + -3x2) = -42 Reorder the terms: -14 + -28 + 13x + 19x + -3x2 + -3x2 = -42 Combine like terms: -14 + -28 = -42 -42 + 13x + 19x + -3x2 + -3x2 = -42 Combine like terms: 13x + 19x = 32x -42 + 32x + -3x2 + -3x2 = -42 Combine like terms: -3x2 + -3x2 = -6x2 -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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