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Simplifying (6x + -5)(2 + -3x) = 0 Reorder the terms: (-5 + 6x)(2 + -3x) = 0 Multiply (-5 + 6x) * (2 + -3x) (-5(2 + -3x) + 6x * (2 + -3x)) = 0 ((2 * -5 + -3x * -5) + 6x * (2 + -3x)) = 0 ((-10 + 15x) + 6x * (2 + -3x)) = 0 (-10 + 15x + (2 * 6x + -3x * 6x)) = 0 (-10 + 15x + (12x + -18x2)) = 0 Combine like terms: 15x + 12x = 27x (-10 + 27x + -18x2) = 0 Solving -10 + 27x + -18x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + 6x)(2 + -3x) = 0Subproblem 1
Set the factor '(-5 + 6x)' equal to zero and attempt to solve: Simplifying -5 + 6x = 0 Solving -5 + 6x = 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 + 6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6x = 0 + 5 6x = 0 + 5 Combine like terms: 0 + 5 = 5 6x = 5 Divide each side by '6'. x = 0.8333333333 Simplifying x = 0.8333333333Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0.8333333333, 0.6666666667}
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