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Simplifying (4x + 7)(6x + -9) = 0 Reorder the terms: (7 + 4x)(6x + -9) = 0 Reorder the terms: (7 + 4x)(-9 + 6x) = 0 Multiply (7 + 4x) * (-9 + 6x) (7(-9 + 6x) + 4x * (-9 + 6x)) = 0 ((-9 * 7 + 6x * 7) + 4x * (-9 + 6x)) = 0 ((-63 + 42x) + 4x * (-9 + 6x)) = 0 (-63 + 42x + (-9 * 4x + 6x * 4x)) = 0 (-63 + 42x + (-36x + 24x2)) = 0 Combine like terms: 42x + -36x = 6x (-63 + 6x + 24x2) = 0 Solving -63 + 6x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 2x + 8x2) = 0 Factor a trinomial. 3((-7 + -4x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve: Simplifying -7 + -4x = 0 Solving -7 + -4x = 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 + -4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4x = 0 + 7 -4x = 0 + 7 Combine like terms: 0 + 7 = 7 -4x = 7 Divide each side by '-4'. x = -1.75 Simplifying x = -1.75Subproblem 2
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 = 1.5Solution
x = {-1.75, 1.5}
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