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Simplifying 2(4x + -2) + 2(2x + 1) = (2x + 1)(4x + -2) Reorder the terms: 2(-2 + 4x) + 2(2x + 1) = (2x + 1)(4x + -2) (-2 * 2 + 4x * 2) + 2(2x + 1) = (2x + 1)(4x + -2) (-4 + 8x) + 2(2x + 1) = (2x + 1)(4x + -2) Reorder the terms: -4 + 8x + 2(1 + 2x) = (2x + 1)(4x + -2) -4 + 8x + (1 * 2 + 2x * 2) = (2x + 1)(4x + -2) -4 + 8x + (2 + 4x) = (2x + 1)(4x + -2) Reorder the terms: -4 + 2 + 8x + 4x = (2x + 1)(4x + -2) Combine like terms: -4 + 2 = -2 -2 + 8x + 4x = (2x + 1)(4x + -2) Combine like terms: 8x + 4x = 12x -2 + 12x = (2x + 1)(4x + -2) Reorder the terms: -2 + 12x = (1 + 2x)(4x + -2) Reorder the terms: -2 + 12x = (1 + 2x)(-2 + 4x) Multiply (1 + 2x) * (-2 + 4x) -2 + 12x = (1(-2 + 4x) + 2x * (-2 + 4x)) -2 + 12x = ((-2 * 1 + 4x * 1) + 2x * (-2 + 4x)) -2 + 12x = ((-2 + 4x) + 2x * (-2 + 4x)) -2 + 12x = (-2 + 4x + (-2 * 2x + 4x * 2x)) -2 + 12x = (-2 + 4x + (-4x + 8x2)) Combine like terms: 4x + -4x = 0 -2 + 12x = (-2 + 0 + 8x2) -2 + 12x = (-2 + 8x2) Add '2' to each side of the equation. -2 + 2 + 12x = -2 + 2 + 8x2 Combine like terms: -2 + 2 = 0 0 + 12x = -2 + 2 + 8x2 12x = -2 + 2 + 8x2 Combine like terms: -2 + 2 = 0 12x = 0 + 8x2 12x = 8x2 Solving 12x = 8x2 Solving for variable 'x'. Combine like terms: 8x2 + -8x2 = 0 12x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + -2x) = 0 Ignore the factor 4.Subproblem 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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