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Simplifying 2(3x + -2)(4x + 7) = 0 Reorder the terms: 2(-2 + 3x)(4x + 7) = 0 Reorder the terms: 2(-2 + 3x)(7 + 4x) = 0 Multiply (-2 + 3x) * (7 + 4x) 2(-2(7 + 4x) + 3x * (7 + 4x)) = 0 2((7 * -2 + 4x * -2) + 3x * (7 + 4x)) = 0 2((-14 + -8x) + 3x * (7 + 4x)) = 0 2(-14 + -8x + (7 * 3x + 4x * 3x)) = 0 2(-14 + -8x + (21x + 12x2)) = 0 Combine like terms: -8x + 21x = 13x 2(-14 + 13x + 12x2) = 0 (-14 * 2 + 13x * 2 + 12x2 * 2) = 0 (-28 + 26x + 24x2) = 0 Solving -28 + 26x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 13x + 12x2) = 0 Factor a trinomial. 2((-7 + -4x)(2 + -3x)) = 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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-1.75, 0.6666666667}
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