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Simplifying 2(7x + -2)(4x + 3) = 0 Reorder the terms: 2(-2 + 7x)(4x + 3) = 0 Reorder the terms: 2(-2 + 7x)(3 + 4x) = 0 Multiply (-2 + 7x) * (3 + 4x) 2(-2(3 + 4x) + 7x * (3 + 4x)) = 0 2((3 * -2 + 4x * -2) + 7x * (3 + 4x)) = 0 2((-6 + -8x) + 7x * (3 + 4x)) = 0 2(-6 + -8x + (3 * 7x + 4x * 7x)) = 0 2(-6 + -8x + (21x + 28x2)) = 0 Combine like terms: -8x + 21x = 13x 2(-6 + 13x + 28x2) = 0 (-6 * 2 + 13x * 2 + 28x2 * 2) = 0 (-12 + 26x + 56x2) = 0 Solving -12 + 26x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 13x + 28x2) = 0 Factor a trinomial. 2((-3 + -4x)(2 + -7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Solution
x = {-0.75, 0.2857142857}
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