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Simplifying (2x2) + 3x + -6 = (-4x2) + 4x + -5 Reorder the terms: -6 + 3x + (2x2) = (-4x2) + 4x + -5 Reorder the terms: -6 + 3x + (2x2) = -5 + 4x + (-4x2) Solving -6 + 3x + (2x2) = -5 + 4x + (-4x2) Solving for variable 'x'. Reorder the terms: -6 + 5 + 3x + -4x + (2x2) + (4x2) = -5 + 4x + (-4x2) + 5 + -4x + (4x2) Combine like terms: -6 + 5 = -1 -1 + 3x + -4x + (2x2) + (4x2) = -5 + 4x + (-4x2) + 5 + -4x + (4x2) Combine like terms: 3x + -4x = -1x -1 + -1x + (2x2) + (4x2) = -5 + 4x + (-4x2) + 5 + -4x + (4x2) Combine like terms: (2x2) + (4x2) = 6x2 -1 + -1x + 6x2 = -5 + 4x + (-4x2) + 5 + -4x + (4x2) Reorder the terms: -1 + -1x + 6x2 = -5 + 5 + 4x + -4x + (-4x2) + (4x2) Combine like terms: -5 + 5 = 0 -1 + -1x + 6x2 = 0 + 4x + -4x + (-4x2) + (4x2) -1 + -1x + 6x2 = 4x + -4x + (-4x2) + (4x2) Combine like terms: 4x + -4x = 0 -1 + -1x + 6x2 = 0 + (-4x2) + (4x2) -1 + -1x + 6x2 = (-4x2) + (4x2) Combine like terms: (-4x2) + (4x2) = 0 -1 + -1x + 6x2 = 0 Factor a trinomial. (-1 + -3x)(1 + -2x) = 0Subproblem 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 '(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 = {-0.3333333333, 0.5}
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