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Simplifying (7b + -4)(7b + 7) = 0 Reorder the terms: (-4 + 7b)(7b + 7) = 0 Reorder the terms: (-4 + 7b)(7 + 7b) = 0 Multiply (-4 + 7b) * (7 + 7b) (-4(7 + 7b) + 7b * (7 + 7b)) = 0 ((7 * -4 + 7b * -4) + 7b * (7 + 7b)) = 0 ((-28 + -28b) + 7b * (7 + 7b)) = 0 (-28 + -28b + (7 * 7b + 7b * 7b)) = 0 (-28 + -28b + (49b + 49b2)) = 0 Combine like terms: -28b + 49b = 21b (-28 + 21b + 49b2) = 0 Solving -28 + 21b + 49b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '7'. 7(-4 + 3b + 7b2) = 0 Factor a trinomial. 7((-1 + -1b)(4 + -7b)) = 0 Ignore the factor 7.Subproblem 1
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 = -1Subproblem 2
Set the factor '(4 + -7b)' equal to zero and attempt to solve: Simplifying 4 + -7b = 0 Solving 4 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7b = 0 + -4 -7b = 0 + -4 Combine like terms: 0 + -4 = -4 -7b = -4 Divide each side by '-7'. b = 0.5714285714 Simplifying b = 0.5714285714Solution
b = {-1, 0.5714285714}
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