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Simplifying 18(3x + 1) = (4x + 4)(2x + 2) Reorder the terms: 18(1 + 3x) = (4x + 4)(2x + 2) (1 * 18 + 3x * 18) = (4x + 4)(2x + 2) (18 + 54x) = (4x + 4)(2x + 2) Reorder the terms: 18 + 54x = (4 + 4x)(2x + 2) Reorder the terms: 18 + 54x = (4 + 4x)(2 + 2x) Multiply (4 + 4x) * (2 + 2x) 18 + 54x = (4(2 + 2x) + 4x * (2 + 2x)) 18 + 54x = ((2 * 4 + 2x * 4) + 4x * (2 + 2x)) 18 + 54x = ((8 + 8x) + 4x * (2 + 2x)) 18 + 54x = (8 + 8x + (2 * 4x + 2x * 4x)) 18 + 54x = (8 + 8x + (8x + 8x2)) Combine like terms: 8x + 8x = 16x 18 + 54x = (8 + 16x + 8x2) Solving 18 + 54x = 8 + 16x + 8x2 Solving for variable 'x'. Reorder the terms: 18 + -8 + 54x + -16x + -8x2 = 8 + 16x + 8x2 + -8 + -16x + -8x2 Combine like terms: 18 + -8 = 10 10 + 54x + -16x + -8x2 = 8 + 16x + 8x2 + -8 + -16x + -8x2 Combine like terms: 54x + -16x = 38x 10 + 38x + -8x2 = 8 + 16x + 8x2 + -8 + -16x + -8x2 Reorder the terms: 10 + 38x + -8x2 = 8 + -8 + 16x + -16x + 8x2 + -8x2 Combine like terms: 8 + -8 = 0 10 + 38x + -8x2 = 0 + 16x + -16x + 8x2 + -8x2 10 + 38x + -8x2 = 16x + -16x + 8x2 + -8x2 Combine like terms: 16x + -16x = 0 10 + 38x + -8x2 = 0 + 8x2 + -8x2 10 + 38x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 10 + 38x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 19x + -4x2) = 0 Factor a trinomial. 2((5 + -1x)(1 + 4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {5, -0.25}
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