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Simplifying (5x + 1)(x + -4) + (x + -4)(x + 1) = 0 Reorder the terms: (1 + 5x)(x + -4) + (x + -4)(x + 1) = 0 Reorder the terms: (1 + 5x)(-4 + x) + (x + -4)(x + 1) = 0 Multiply (1 + 5x) * (-4 + x) (1(-4 + x) + 5x * (-4 + x)) + (x + -4)(x + 1) = 0 ((-4 * 1 + x * 1) + 5x * (-4 + x)) + (x + -4)(x + 1) = 0 ((-4 + 1x) + 5x * (-4 + x)) + (x + -4)(x + 1) = 0 (-4 + 1x + (-4 * 5x + x * 5x)) + (x + -4)(x + 1) = 0 (-4 + 1x + (-20x + 5x2)) + (x + -4)(x + 1) = 0 Combine like terms: 1x + -20x = -19x (-4 + -19x + 5x2) + (x + -4)(x + 1) = 0 Reorder the terms: -4 + -19x + 5x2 + (-4 + x)(x + 1) = 0 Reorder the terms: -4 + -19x + 5x2 + (-4 + x)(1 + x) = 0 Multiply (-4 + x) * (1 + x) -4 + -19x + 5x2 + (-4(1 + x) + x(1 + x)) = 0 -4 + -19x + 5x2 + ((1 * -4 + x * -4) + x(1 + x)) = 0 -4 + -19x + 5x2 + ((-4 + -4x) + x(1 + x)) = 0 -4 + -19x + 5x2 + (-4 + -4x + (1 * x + x * x)) = 0 -4 + -19x + 5x2 + (-4 + -4x + (1x + x2)) = 0 Combine like terms: -4x + 1x = -3x -4 + -19x + 5x2 + (-4 + -3x + x2) = 0 Reorder the terms: -4 + -4 + -19x + -3x + 5x2 + x2 = 0 Combine like terms: -4 + -4 = -8 -8 + -19x + -3x + 5x2 + x2 = 0 Combine like terms: -19x + -3x = -22x -8 + -22x + 5x2 + x2 = 0 Combine like terms: 5x2 + x2 = 6x2 -8 + -22x + 6x2 = 0 Solving -8 + -22x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -11x + 3x2) = 0 Factor a trinomial. 2((-1 + -3x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.3333333333, 4}
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