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Simplifying x(x + 7) = 3(x + 4) Reorder the terms: x(7 + x) = 3(x + 4) (7 * x + x * x) = 3(x + 4) (7x + x2) = 3(x + 4) Reorder the terms: 7x + x2 = 3(4 + x) 7x + x2 = (4 * 3 + x * 3) 7x + x2 = (12 + 3x) Solving 7x + x2 = 12 + 3x Solving for variable 'x'. Reorder the terms: -12 + 7x + -3x + x2 = 12 + 3x + -12 + -3x Combine like terms: 7x + -3x = 4x -12 + 4x + x2 = 12 + 3x + -12 + -3x Reorder the terms: -12 + 4x + x2 = 12 + -12 + 3x + -3x Combine like terms: 12 + -12 = 0 -12 + 4x + x2 = 0 + 3x + -3x -12 + 4x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -12 + 4x + x2 = 0 Factor a trinomial. (-6 + -1x)(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-6, 2}
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