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Simplifying (x + -3)(x + 5) = 7x + -15 Reorder the terms: (-3 + x)(x + 5) = 7x + -15 Reorder the terms: (-3 + x)(5 + x) = 7x + -15 Multiply (-3 + x) * (5 + x) (-3(5 + x) + x(5 + x)) = 7x + -15 ((5 * -3 + x * -3) + x(5 + x)) = 7x + -15 ((-15 + -3x) + x(5 + x)) = 7x + -15 (-15 + -3x + (5 * x + x * x)) = 7x + -15 (-15 + -3x + (5x + x2)) = 7x + -15 Combine like terms: -3x + 5x = 2x (-15 + 2x + x2) = 7x + -15 Reorder the terms: -15 + 2x + x2 = -15 + 7x Add '15' to each side of the equation. -15 + 2x + 15 + x2 = -15 + 15 + 7x Reorder the terms: -15 + 15 + 2x + x2 = -15 + 15 + 7x Combine like terms: -15 + 15 = 0 0 + 2x + x2 = -15 + 15 + 7x 2x + x2 = -15 + 15 + 7x Combine like terms: -15 + 15 = 0 2x + x2 = 0 + 7x 2x + x2 = 7x Solving 2x + x2 = 7x Solving for variable 'x'. Reorder the terms: 2x + -7x + x2 = 7x + -7x Combine like terms: 2x + -7x = -5x -5x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -5x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 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 '(-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 = 5Solution
x = {0, 5}
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