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Simplifying (4x + -3)(6x + -6) = 0 Reorder the terms: (-3 + 4x)(6x + -6) = 0 Reorder the terms: (-3 + 4x)(-6 + 6x) = 0 Multiply (-3 + 4x) * (-6 + 6x) (-3(-6 + 6x) + 4x * (-6 + 6x)) = 0 ((-6 * -3 + 6x * -3) + 4x * (-6 + 6x)) = 0 ((18 + -18x) + 4x * (-6 + 6x)) = 0 (18 + -18x + (-6 * 4x + 6x * 4x)) = 0 (18 + -18x + (-24x + 24x2)) = 0 Combine like terms: -18x + -24x = -42x (18 + -42x + 24x2) = 0 Solving 18 + -42x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(3 + -7x + 4x2) = 0 Factor a trinomial. 6((3 + -4x)(1 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 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 = {0.75, 1}
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