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Simplifying 3x(x + 2) + -4 = (x + 4)(2x + -1) Reorder the terms: 3x(2 + x) + -4 = (x + 4)(2x + -1) (2 * 3x + x * 3x) + -4 = (x + 4)(2x + -1) (6x + 3x2) + -4 = (x + 4)(2x + -1) Reorder the terms: -4 + 6x + 3x2 = (x + 4)(2x + -1) Reorder the terms: -4 + 6x + 3x2 = (4 + x)(2x + -1) Reorder the terms: -4 + 6x + 3x2 = (4 + x)(-1 + 2x) Multiply (4 + x) * (-1 + 2x) -4 + 6x + 3x2 = (4(-1 + 2x) + x(-1 + 2x)) -4 + 6x + 3x2 = ((-1 * 4 + 2x * 4) + x(-1 + 2x)) -4 + 6x + 3x2 = ((-4 + 8x) + x(-1 + 2x)) -4 + 6x + 3x2 = (-4 + 8x + (-1 * x + 2x * x)) -4 + 6x + 3x2 = (-4 + 8x + (-1x + 2x2)) Combine like terms: 8x + -1x = 7x -4 + 6x + 3x2 = (-4 + 7x + 2x2) Add '4' to each side of the equation. -4 + 6x + 4 + 3x2 = -4 + 7x + 4 + 2x2 Reorder the terms: -4 + 4 + 6x + 3x2 = -4 + 7x + 4 + 2x2 Combine like terms: -4 + 4 = 0 0 + 6x + 3x2 = -4 + 7x + 4 + 2x2 6x + 3x2 = -4 + 7x + 4 + 2x2 Reorder the terms: 6x + 3x2 = -4 + 4 + 7x + 2x2 Combine like terms: -4 + 4 = 0 6x + 3x2 = 0 + 7x + 2x2 6x + 3x2 = 7x + 2x2 Solving 6x + 3x2 = 7x + 2x2 Solving for variable 'x'. Reorder the terms: 6x + -7x + 3x2 + -2x2 = 7x + 2x2 + -7x + -2x2 Combine like terms: 6x + -7x = -1x -1x + 3x2 + -2x2 = 7x + 2x2 + -7x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -1x + 1x2 = 7x + 2x2 + -7x + -2x2 Reorder the terms: -1x + 1x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -1x + 1x2 = 0 + 2x2 + -2x2 -1x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + x) = 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 '(-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 = {0, 1}
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