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