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Simplifying (x + -26)(4x + 3)(52x) = 0 Reorder the terms: (-26 + x)(4x + 3)(52x) = 0 Reorder the terms: (-26 + x)(3 + 4x)(52x) = 0 Remove parenthesis around (52x) (-26 + x)(3 + 4x) * 52x = 0 Reorder the terms for easier multiplication: 52x(-26 + x)(3 + 4x) = 0 Multiply (-26 + x) * (3 + 4x) 52x(-26(3 + 4x) + x(3 + 4x)) = 0 52x((3 * -26 + 4x * -26) + x(3 + 4x)) = 0 52x((-78 + -104x) + x(3 + 4x)) = 0 52x(-78 + -104x + (3 * x + 4x * x)) = 0 52x(-78 + -104x + (3x + 4x2)) = 0 Combine like terms: -104x + 3x = -101x 52x(-78 + -101x + 4x2) = 0 (-78 * 52x + -101x * 52x + 4x2 * 52x) = 0 (-4056x + -5252x2 + 208x3) = 0 Solving -4056x + -5252x2 + 208x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '52x'. 52x(-78 + -101x + 4x2) = 0 Factor a trinomial. 52x((-3 + -4x)(26 + -1x)) = 0 Ignore the factor 52.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
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 3
Set the factor '(26 + -1x)' equal to zero and attempt to solve: Simplifying 26 + -1x = 0 Solving 26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + -1x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -1x = 0 + -26 -1x = 0 + -26 Combine like terms: 0 + -26 = -26 -1x = -26 Divide each side by '-1'. x = 26 Simplifying x = 26Solution
x = {0, -0.75, 26}
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