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Simplifying (4x + -6)(x + -6)(3) = 0 Reorder the terms: (-6 + 4x)(x + -6)(3) = 0 Reorder the terms: (-6 + 4x)(-6 + x)(3) = 0 Reorder the terms for easier multiplication: 3(-6 + 4x)(-6 + x) = 0 Multiply (-6 + 4x) * (-6 + x) 3(-6(-6 + x) + 4x * (-6 + x)) = 0 3((-6 * -6 + x * -6) + 4x * (-6 + x)) = 0 3((36 + -6x) + 4x * (-6 + x)) = 0 3(36 + -6x + (-6 * 4x + x * 4x)) = 0 3(36 + -6x + (-24x + 4x2)) = 0 Combine like terms: -6x + -24x = -30x 3(36 + -30x + 4x2) = 0 (36 * 3 + -30x * 3 + 4x2 * 3) = 0 (108 + -90x + 12x2) = 0 Solving 108 + -90x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(18 + -15x + 2x2) = 0 Factor a trinomial. 6((3 + -2x)(6 + -1x)) = 0 Ignore the factor 6.Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {1.5, 6}
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