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Simplifying (p + -5) * x(5p + -6) = 0 Reorder the terms: (-5 + p) * x(5p + -6) = 0 Reorder the terms: (-5 + p) * x(-6 + 5p) = 0 Reorder the terms for easier multiplication: x(-5 + p)(-6 + 5p) = 0 Multiply (-5 + p) * (-6 + 5p) x(-5(-6 + 5p) + p(-6 + 5p)) = 0 x((-6 * -5 + 5p * -5) + p(-6 + 5p)) = 0 x((30 + -25p) + p(-6 + 5p)) = 0 x(30 + -25p + (-6 * p + 5p * p)) = 0 x(30 + -25p + (-6p + 5p2)) = 0 Combine like terms: -25p + -6p = -31p x(30 + -31p + 5p2) = 0 (30 * x + -31p * x + 5p2 * x) = 0 Reorder the terms: (-31px + 5p2x + 30x) = 0 (-31px + 5p2x + 30x) = 0 Solving -31px + 5p2x + 30x = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'x'. x(-31p + 5p2 + 30) = 0 Factor a trinomial. x((p + -5)(5p + -6)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing p to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(p + -5)' equal to zero and attempt to solve: Simplifying p + -5 = 0 Reorder the terms: -5 + p = 0 Solving -5 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + p = 0 + 5 p = 0 + 5 Combine like terms: 0 + 5 = 5 p = 5 Simplifying p = 5Subproblem 3
Set the factor '(5p + -6)' equal to zero and attempt to solve: Simplifying 5p + -6 = 0 Reorder the terms: -6 + 5p = 0 Solving -6 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 5p = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5p = 0 + 6 5p = 0 + 6 Combine like terms: 0 + 6 = 6 5p = 6 Divide each side by '5'. p = 1.2 Simplifying p = 1.2Solution
p = {5, 1.2}
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