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Simplifying 7b2 + 2b + 4 = 6b2 + 7 Reorder the terms: 4 + 2b + 7b2 = 6b2 + 7 Reorder the terms: 4 + 2b + 7b2 = 7 + 6b2 Solving 4 + 2b + 7b2 = 7 + 6b2 Solving for variable 'b'. Reorder the terms: 4 + -7 + 2b + 7b2 + -6b2 = 7 + 6b2 + -7 + -6b2 Combine like terms: 4 + -7 = -3 -3 + 2b + 7b2 + -6b2 = 7 + 6b2 + -7 + -6b2 Combine like terms: 7b2 + -6b2 = 1b2 -3 + 2b + 1b2 = 7 + 6b2 + -7 + -6b2 Reorder the terms: -3 + 2b + 1b2 = 7 + -7 + 6b2 + -6b2 Combine like terms: 7 + -7 = 0 -3 + 2b + 1b2 = 0 + 6b2 + -6b2 -3 + 2b + 1b2 = 6b2 + -6b2 Combine like terms: 6b2 + -6b2 = 0 -3 + 2b + 1b2 = 0 Factor a trinomial. (-3 + -1b)(1 + -1b) = 0Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1Solution
b = {-3, 1}
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