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Simplifying (10x + 7)(3x + -9) = 0 Reorder the terms: (7 + 10x)(3x + -9) = 0 Reorder the terms: (7 + 10x)(-9 + 3x) = 0 Multiply (7 + 10x) * (-9 + 3x) (7(-9 + 3x) + 10x * (-9 + 3x)) = 0 ((-9 * 7 + 3x * 7) + 10x * (-9 + 3x)) = 0 ((-63 + 21x) + 10x * (-9 + 3x)) = 0 (-63 + 21x + (-9 * 10x + 3x * 10x)) = 0 (-63 + 21x + (-90x + 30x2)) = 0 Combine like terms: 21x + -90x = -69x (-63 + -69x + 30x2) = 0 Solving -63 + -69x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -23x + 10x2) = 0 Factor a trinomial. 3((-7 + -10x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -10x)' equal to zero and attempt to solve: Simplifying -7 + -10x = 0 Solving -7 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -10x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10x = 0 + 7 -10x = 0 + 7 Combine like terms: 0 + 7 = 7 -10x = 7 Divide each side by '-10'. x = -0.7 Simplifying x = -0.7Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-0.7, 3}
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