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Simplifying (5x + 2)(x + 1) + (3x + 3)(x + -2) = 0 Reorder the terms: (2 + 5x)(x + 1) + (3x + 3)(x + -2) = 0 Reorder the terms: (2 + 5x)(1 + x) + (3x + 3)(x + -2) = 0 Multiply (2 + 5x) * (1 + x) (2(1 + x) + 5x * (1 + x)) + (3x + 3)(x + -2) = 0 ((1 * 2 + x * 2) + 5x * (1 + x)) + (3x + 3)(x + -2) = 0 ((2 + 2x) + 5x * (1 + x)) + (3x + 3)(x + -2) = 0 (2 + 2x + (1 * 5x + x * 5x)) + (3x + 3)(x + -2) = 0 (2 + 2x + (5x + 5x2)) + (3x + 3)(x + -2) = 0 Combine like terms: 2x + 5x = 7x (2 + 7x + 5x2) + (3x + 3)(x + -2) = 0 Reorder the terms: 2 + 7x + 5x2 + (3 + 3x)(x + -2) = 0 Reorder the terms: 2 + 7x + 5x2 + (3 + 3x)(-2 + x) = 0 Multiply (3 + 3x) * (-2 + x) 2 + 7x + 5x2 + (3(-2 + x) + 3x * (-2 + x)) = 0 2 + 7x + 5x2 + ((-2 * 3 + x * 3) + 3x * (-2 + x)) = 0 2 + 7x + 5x2 + ((-6 + 3x) + 3x * (-2 + x)) = 0 2 + 7x + 5x2 + (-6 + 3x + (-2 * 3x + x * 3x)) = 0 2 + 7x + 5x2 + (-6 + 3x + (-6x + 3x2)) = 0 Combine like terms: 3x + -6x = -3x 2 + 7x + 5x2 + (-6 + -3x + 3x2) = 0 Reorder the terms: 2 + -6 + 7x + -3x + 5x2 + 3x2 = 0 Combine like terms: 2 + -6 = -4 -4 + 7x + -3x + 5x2 + 3x2 = 0 Combine like terms: 7x + -3x = 4x -4 + 4x + 5x2 + 3x2 = 0 Combine like terms: 5x2 + 3x2 = 8x2 -4 + 4x + 8x2 = 0 Solving -4 + 4x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + x + 2x2) = 0 Factor a trinomial. 4((-1 + -1x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-1, 0.5}
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