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Simplifying (2x + -6)(4x + 7) = 0 Reorder the terms: (-6 + 2x)(4x + 7) = 0 Reorder the terms: (-6 + 2x)(7 + 4x) = 0 Multiply (-6 + 2x) * (7 + 4x) (-6(7 + 4x) + 2x * (7 + 4x)) = 0 ((7 * -6 + 4x * -6) + 2x * (7 + 4x)) = 0 ((-42 + -24x) + 2x * (7 + 4x)) = 0 (-42 + -24x + (7 * 2x + 4x * 2x)) = 0 (-42 + -24x + (14x + 8x2)) = 0 Combine like terms: -24x + 14x = -10x (-42 + -10x + 8x2) = 0 Solving -42 + -10x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -5x + 4x2) = 0 Factor a trinomial. 2((-7 + -4x)(3 + -1x)) = 0 Ignore the factor 2.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 + -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 = {-1.75, 3}
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