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Simplifying 5x2 + -3x + 3(1 + -2) = 2(4 + -2) * x2 + -1(7 + -10)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Combine like terms: 1 + -2 = -1 5x2 + -3x + 3(-1) = 2(4 + -2) * x2 + -1(7 + -10)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Multiply 3 * -1 5x2 + -3x + -3 = 2(4 + -2) * x2 + -1(7 + -10)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Reorder the terms: -3 + -3x + 5x2 = 2(4 + -2) * x2 + -1(7 + -10)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Combine like terms: 4 + -2 = 2 -3 + -3x + 5x2 = 2(2) * x2 + -1(7 + -10)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Multiply 2 * 2 -3 + -3x + 5x2 = 4x2 + -1(7 + -10)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Combine like terms: 7 + -10 = -3 -3 + -3x + 5x2 = 4x2 + -1(-3)(3 + -2(4 + -3)) + -1(2 + -2(3 + -4)) * x Combine like terms: 4 + -3 = 1 -3 + -3x + 5x2 = 4x2 + -1 * -3(3 + -2(1)) + -1(2 + -2(3 + -4)) * x Multiply -2 * 1 -3 + -3x + 5x2 = 4x2 + -1 * -3(3 + -2) + -1(2 + -2(3 + -4)) * x Combine like terms: 3 + -2 = 1 -3 + -3x + 5x2 = 4x2 + -1 * -3(1) + -1(2 + -2(3 + -4)) * x Multiply -1 * -3 -3 + -3x + 5x2 = 4x2 + 3 * 1 + -1(2 + -2(3 + -4)) * x Multiply 3 * 1 -3 + -3x + 5x2 = 4x2 + 3 + -1(2 + -2(3 + -4)) * x Combine like terms: 3 + -4 = -1 -3 + -3x + 5x2 = 4x2 + 3 + -1(2 + -2(-1)) * x Multiply -2 * -1 -3 + -3x + 5x2 = 4x2 + 3 + -1(2 + 2) * x Combine like terms: 2 + 2 = 4 -3 + -3x + 5x2 = 4x2 + 3 + -1(4) * x Multiply -1 * 4 -3 + -3x + 5x2 = 4x2 + 3 + -4x Reorder the terms: -3 + -3x + 5x2 = 3 + -4x + 4x2 Solving -3 + -3x + 5x2 = 3 + -4x + 4x2 Solving for variable 'x'. Reorder the terms: -3 + -3 + -3x + 4x + 5x2 + -4x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2 Combine like terms: -3 + -3 = -6 -6 + -3x + 4x + 5x2 + -4x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2 Combine like terms: -3x + 4x = 1x -6 + 1x + 5x2 + -4x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 -6 + 1x + 1x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2 Reorder the terms: -6 + 1x + 1x2 = 3 + -3 + -4x + 4x + 4x2 + -4x2 Combine like terms: 3 + -3 = 0 -6 + 1x + 1x2 = 0 + -4x + 4x + 4x2 + -4x2 -6 + 1x + 1x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 -6 + 1x + 1x2 = 0 + 4x2 + -4x2 -6 + 1x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -6 + 1x + 1x2 = 0 Factor a trinomial. (-3 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-3, 2}
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