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Simplifying (14b + 9)(5b + -15) = 0 Reorder the terms: (9 + 14b)(5b + -15) = 0 Reorder the terms: (9 + 14b)(-15 + 5b) = 0 Multiply (9 + 14b) * (-15 + 5b) (9(-15 + 5b) + 14b * (-15 + 5b)) = 0 ((-15 * 9 + 5b * 9) + 14b * (-15 + 5b)) = 0 ((-135 + 45b) + 14b * (-15 + 5b)) = 0 (-135 + 45b + (-15 * 14b + 5b * 14b)) = 0 (-135 + 45b + (-210b + 70b2)) = 0 Combine like terms: 45b + -210b = -165b (-135 + -165b + 70b2) = 0 Solving -135 + -165b + 70b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5'. 5(-27 + -33b + 14b2) = 0 Factor a trinomial. 5((-9 + -14b)(3 + -1b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -14b)' equal to zero and attempt to solve: Simplifying -9 + -14b = 0 Solving -9 + -14b = 0 Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -14b = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -14b = 0 + 9 -14b = 0 + 9 Combine like terms: 0 + 9 = 9 -14b = 9 Divide each side by '-14'. b = -0.6428571429 Simplifying b = -0.6428571429Subproblem 2
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 = 3Solution
b = {-0.6428571429, 3}
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