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Simplifying (9x + -10)(3x + -6) = 0 Reorder the terms: (-10 + 9x)(3x + -6) = 0 Reorder the terms: (-10 + 9x)(-6 + 3x) = 0 Multiply (-10 + 9x) * (-6 + 3x) (-10(-6 + 3x) + 9x * (-6 + 3x)) = 0 ((-6 * -10 + 3x * -10) + 9x * (-6 + 3x)) = 0 ((60 + -30x) + 9x * (-6 + 3x)) = 0 (60 + -30x + (-6 * 9x + 3x * 9x)) = 0 (60 + -30x + (-54x + 27x2)) = 0 Combine like terms: -30x + -54x = -84x (60 + -84x + 27x2) = 0 Solving 60 + -84x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(20 + -28x + 9x2) = 0 Factor a trinomial. 3((10 + -9x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -9x)' equal to zero and attempt to solve: Simplifying 10 + -9x = 0 Solving 10 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -9x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -9x = 0 + -10 -9x = 0 + -10 Combine like terms: 0 + -10 = -10 -9x = -10 Divide each side by '-9'. x = 1.111111111 Simplifying x = 1.111111111Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {1.111111111, 2}
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