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Simplifying 5(5n + 3) * w + -7 = -22 + -5n Reorder the terms: 5(3 + 5n) * w + -7 = -22 + -5n Reorder the terms for easier multiplication: 5w(3 + 5n) + -7 = -22 + -5n (3 * 5w + 5n * 5w) + -7 = -22 + -5n Reorder the terms: (25nw + 15w) + -7 = -22 + -5n (25nw + 15w) + -7 = -22 + -5n Reorder the terms: -7 + 25nw + 15w = -22 + -5n Solving -7 + 25nw + 15w = -22 + -5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5n' to each side of the equation. -7 + 25nw + 5n + 15w = -22 + -5n + 5n Reorder the terms: -7 + 5n + 25nw + 15w = -22 + -5n + 5n Combine like terms: -5n + 5n = 0 -7 + 5n + 25nw + 15w = -22 + 0 -7 + 5n + 25nw + 15w = -22 Add '7' to each side of the equation. -7 + 5n + 25nw + 7 + 15w = -22 + 7 Reorder the terms: -7 + 7 + 5n + 25nw + 15w = -22 + 7 Combine like terms: -7 + 7 = 0 0 + 5n + 25nw + 15w = -22 + 7 5n + 25nw + 15w = -22 + 7 Combine like terms: -22 + 7 = -15 5n + 25nw + 15w = -15 Add '-15w' to each side of the equation. 5n + 25nw + 15w + -15w = -15 + -15w Combine like terms: 15w + -15w = 0 5n + 25nw + 0 = -15 + -15w 5n + 25nw = -15 + -15w Reorder the terms: 15 + 5n + 25nw + 15w = -15 + -15w + 15 + 15w Reorder the terms: 15 + 5n + 25nw + 15w = -15 + 15 + -15w + 15w Combine like terms: -15 + 15 = 0 15 + 5n + 25nw + 15w = 0 + -15w + 15w 15 + 5n + 25nw + 15w = -15w + 15w Combine like terms: -15w + 15w = 0 15 + 5n + 25nw + 15w = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + n + 5nw + 3w) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + n + 5nw + 3w)' equal to zero and attempt to solve: Simplifying 3 + n + 5nw + 3w = 0 Solving 3 + n + 5nw + 3w = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + n + 5nw + -3 + 3w = 0 + -3 Reorder the terms: 3 + -3 + n + 5nw + 3w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n + 5nw + 3w = 0 + -3 n + 5nw + 3w = 0 + -3 Combine like terms: 0 + -3 = -3 n + 5nw + 3w = -3 Add '-3w' to each side of the equation. n + 5nw + 3w + -3w = -3 + -3w Combine like terms: 3w + -3w = 0 n + 5nw + 0 = -3 + -3w n + 5nw = -3 + -3w The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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