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Simplifying 5x^{2}= 29x + 6 Reorder the terms: 5x^{2}= 6 + 29x Solving 5x^{2}= 6 + 29x Solving for variable 'x'. Reorder the terms: -6 + -29x + 5x^{2}= 6 + 29x + -6 + -29x Reorder the terms: -6 + -29x + 5x^{2}= 6 + -6 + 29x + -29x Combine like terms: 6 + -6 = 0 -6 + -29x + 5x^{2}= 0 + 29x + -29x -6 + -29x + 5x^{2}= 29x + -29x Combine like terms: 29x + -29x = 0 -6 + -29x + 5x^{2}= 0 Factor a trinomial. (-1 + -5x)(6 + -1x) = 0## Subproblem 1

Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2## Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6## Solution

x = {-0.2, 6}

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