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Simplifying 2(x + -3) * 4 + (2x) * 7 + x(x + -3) = 2x(x + -3) Reorder the terms: 2(-3 + x) * 4 + (2x) * 7 + x(x + -3) = 2x(x + -3) Reorder the terms for easier multiplication: 2 * 4(-3 + x) + (2x) * 7 + x(x + -3) = 2x(x + -3) Multiply 2 * 4 8(-3 + x) + (2x) * 7 + x(x + -3) = 2x(x + -3) (-3 * 8 + x * 8) + (2x) * 7 + x(x + -3) = 2x(x + -3) (-24 + 8x) + (2x) * 7 + x(x + -3) = 2x(x + -3) Remove parenthesis around (2x) -24 + 8x + 2x * 7 + x(x + -3) = 2x(x + -3) Reorder the terms for easier multiplication: -24 + 8x + 2 * 7x + x(x + -3) = 2x(x + -3) Multiply 2 * 7 -24 + 8x + 14x + x(x + -3) = 2x(x + -3) Reorder the terms: -24 + 8x + 14x + x(-3 + x) = 2x(x + -3) -24 + 8x + 14x + (-3 * x + x * x) = 2x(x + -3) -24 + 8x + 14x + (-3x + x2) = 2x(x + -3) Combine like terms: 8x + 14x = 22x -24 + 22x + -3x + x2 = 2x(x + -3) Combine like terms: 22x + -3x = 19x -24 + 19x + x2 = 2x(x + -3) Reorder the terms: -24 + 19x + x2 = 2x(-3 + x) -24 + 19x + x2 = (-3 * 2x + x * 2x) -24 + 19x + x2 = (-6x + 2x2) Solving -24 + 19x + x2 = -6x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + 19x + 6x + x2 + -2x2 = -6x + 2x2 + 6x + -2x2 Combine like terms: 19x + 6x = 25x -24 + 25x + x2 + -2x2 = -6x + 2x2 + 6x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -24 + 25x + -1x2 = -6x + 2x2 + 6x + -2x2 Reorder the terms: -24 + 25x + -1x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 -24 + 25x + -1x2 = 0 + 2x2 + -2x2 -24 + 25x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -24 + 25x + -1x2 = 0 Factor a trinomial. (-24 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-24 + x)' equal to zero and attempt to solve: Simplifying -24 + x = 0 Solving -24 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + x = 0 + 24 x = 0 + 24 Combine like terms: 0 + 24 = 24 x = 24 Simplifying x = 24Subproblem 2
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 = 1Solution
x = {24, 1}
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