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Simplifying (2x + 1)(x + -3) + -2x = 2(x + -1) * 2 + 1 Reorder the terms: (1 + 2x)(x + -3) + -2x = 2(x + -1) * 2 + 1 Reorder the terms: (1 + 2x)(-3 + x) + -2x = 2(x + -1) * 2 + 1 Multiply (1 + 2x) * (-3 + x) (1(-3 + x) + 2x * (-3 + x)) + -2x = 2(x + -1) * 2 + 1 ((-3 * 1 + x * 1) + 2x * (-3 + x)) + -2x = 2(x + -1) * 2 + 1 ((-3 + 1x) + 2x * (-3 + x)) + -2x = 2(x + -1) * 2 + 1 (-3 + 1x + (-3 * 2x + x * 2x)) + -2x = 2(x + -1) * 2 + 1 (-3 + 1x + (-6x + 2x2)) + -2x = 2(x + -1) * 2 + 1 Combine like terms: 1x + -6x = -5x (-3 + -5x + 2x2) + -2x = 2(x + -1) * 2 + 1 Reorder the terms: -3 + -5x + -2x + 2x2 = 2(x + -1) * 2 + 1 Combine like terms: -5x + -2x = -7x -3 + -7x + 2x2 = 2(x + -1) * 2 + 1 Reorder the terms: -3 + -7x + 2x2 = 2(-1 + x) * 2 + 1 Reorder the terms for easier multiplication: -3 + -7x + 2x2 = 2 * 2(-1 + x) + 1 Multiply 2 * 2 -3 + -7x + 2x2 = 4(-1 + x) + 1 -3 + -7x + 2x2 = (-1 * 4 + x * 4) + 1 -3 + -7x + 2x2 = (-4 + 4x) + 1 Reorder the terms: -3 + -7x + 2x2 = -4 + 1 + 4x Combine like terms: -4 + 1 = -3 -3 + -7x + 2x2 = -3 + 4x Add '3' to each side of the equation. -3 + -7x + 3 + 2x2 = -3 + 3 + 4x Reorder the terms: -3 + 3 + -7x + 2x2 = -3 + 3 + 4x Combine like terms: -3 + 3 = 0 0 + -7x + 2x2 = -3 + 3 + 4x -7x + 2x2 = -3 + 3 + 4x Combine like terms: -3 + 3 = 0 -7x + 2x2 = 0 + 4x -7x + 2x2 = 4x Solving -7x + 2x2 = 4x Solving for variable 'x'. Reorder the terms: -7x + -4x + 2x2 = 4x + -4x Combine like terms: -7x + -4x = -11x -11x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -11x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Divide each side by '2'. x = 5.5 Simplifying x = 5.5Solution
x = {0, 5.5}
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