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Simplifying (8 + 2x)(10 + 2x) = 0 Multiply (8 + 2x) * (10 + 2x) (8(10 + 2x) + 2x * (10 + 2x)) = 0 ((10 * 8 + 2x * 8) + 2x * (10 + 2x)) = 0 ((80 + 16x) + 2x * (10 + 2x)) = 0 (80 + 16x + (10 * 2x + 2x * 2x)) = 0 (80 + 16x + (20x + 4x2)) = 0 Combine like terms: 16x + 20x = 36x (80 + 36x + 4x2) = 0 Solving 80 + 36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(20 + 9x + x2) = 0 Factor a trinomial. 4((5 + x)(4 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-5, -4}
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