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Simplifying 5x(x + 6) = 7x + 42 Reorder the terms: 5x(6 + x) = 7x + 42 (6 * 5x + x * 5x) = 7x + 42 (30x + 5x2) = 7x + 42 Reorder the terms: 30x + 5x2 = 42 + 7x Solving 30x + 5x2 = 42 + 7x Solving for variable 'x'. Reorder the terms: -42 + 30x + -7x + 5x2 = 42 + 7x + -42 + -7x Combine like terms: 30x + -7x = 23x -42 + 23x + 5x2 = 42 + 7x + -42 + -7x Reorder the terms: -42 + 23x + 5x2 = 42 + -42 + 7x + -7x Combine like terms: 42 + -42 = 0 -42 + 23x + 5x2 = 0 + 7x + -7x -42 + 23x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -42 + 23x + 5x2 = 0 Factor a trinomial. (-6 + -1x)(7 + -5x) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {-6, 1.4}
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