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Simplifying (2x + 7)(4x + -8) = 0 Reorder the terms: (7 + 2x)(4x + -8) = 0 Reorder the terms: (7 + 2x)(-8 + 4x) = 0 Multiply (7 + 2x) * (-8 + 4x) (7(-8 + 4x) + 2x * (-8 + 4x)) = 0 ((-8 * 7 + 4x * 7) + 2x * (-8 + 4x)) = 0 ((-56 + 28x) + 2x * (-8 + 4x)) = 0 (-56 + 28x + (-8 * 2x + 4x * 2x)) = 0 (-56 + 28x + (-16x + 8x2)) = 0 Combine like terms: 28x + -16x = 12x (-56 + 12x + 8x2) = 0 Solving -56 + 12x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 3x + 2x2) = 0 Factor a trinomial. 4((-7 + -2x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 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 = {-3.5, 2}
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