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Simplifying (3x + -7)(8x + 4) = 0 Reorder the terms: (-7 + 3x)(8x + 4) = 0 Reorder the terms: (-7 + 3x)(4 + 8x) = 0 Multiply (-7 + 3x) * (4 + 8x) (-7(4 + 8x) + 3x * (4 + 8x)) = 0 ((4 * -7 + 8x * -7) + 3x * (4 + 8x)) = 0 ((-28 + -56x) + 3x * (4 + 8x)) = 0 (-28 + -56x + (4 * 3x + 8x * 3x)) = 0 (-28 + -56x + (12x + 24x2)) = 0 Combine like terms: -56x + 12x = -44x (-28 + -44x + 24x2) = 0 Solving -28 + -44x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + -11x + 6x2) = 0 Factor a trinomial. 4((-1 + -2x)(7 + -3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 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 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-0.5, 2.333333333}
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