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Simplifying (x + 7) * x(x + 7) = 0 Reorder the terms: (7 + x) * x(x + 7) = 0 Reorder the terms: (7 + x) * x(7 + x) = 0 Reorder the terms for easier multiplication: x(7 + x)(7 + x) = 0 Multiply (7 + x) * (7 + x) x(7(7 + x) + x(7 + x)) = 0 x((7 * 7 + x * 7) + x(7 + x)) = 0 x((49 + 7x) + x(7 + x)) = 0 x(49 + 7x + (7 * x + x * x)) = 0 x(49 + 7x + (7x + x2)) = 0 Combine like terms: 7x + 7x = 14x x(49 + 14x + x2) = 0 (49 * x + 14x * x + x2 * x) = 0 (49x + 14x2 + x3) = 0 Solving 49x + 14x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(49 + 14x + x2) = 0 Factor a trinomial. x((7 + x)(7 + x)) = 0Subproblem 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 3
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {0, -7, -7}
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