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Simplifying (6x + -3)(4x + 5 + -1x) = 0 Reorder the terms: (-3 + 6x)(4x + 5 + -1x) = 0 Reorder the terms: (-3 + 6x)(5 + 4x + -1x) = 0 Combine like terms: 4x + -1x = 3x (-3 + 6x)(5 + 3x) = 0 Multiply (-3 + 6x) * (5 + 3x) (-3(5 + 3x) + 6x * (5 + 3x)) = 0 ((5 * -3 + 3x * -3) + 6x * (5 + 3x)) = 0 ((-15 + -9x) + 6x * (5 + 3x)) = 0 (-15 + -9x + (5 * 6x + 3x * 6x)) = 0 (-15 + -9x + (30x + 18x2)) = 0 Combine like terms: -9x + 30x = 21x (-15 + 21x + 18x2) = 0 Solving -15 + 21x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 7x + 6x2) = 0 Factor a trinomial. 3((-5 + -3x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 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 = {-1.666666667, 0.5}
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