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Simplifying 1 + 6x = 4x(3 + -2x) 1 + 6x = (3 * 4x + -2x * 4x) 1 + 6x = (12x + -8x2) Solving 1 + 6x = 12x + -8x2 Solving for variable 'x'. Combine like terms: 6x + -12x = -6x 1 + -6x + 8x2 = 12x + -8x2 + -12x + 8x2 Reorder the terms: 1 + -6x + 8x2 = 12x + -12x + -8x2 + 8x2 Combine like terms: 12x + -12x = 0 1 + -6x + 8x2 = 0 + -8x2 + 8x2 1 + -6x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 1 + -6x + 8x2 = 0 Factor a trinomial. (1 + -4x)(1 + -2x) = 0Subproblem 1
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 = 0.25Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0.25, 0.5}
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