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Simplifying (4a + -15)(7a + 23) = 0 Reorder the terms: (-15 + 4a)(7a + 23) = 0 Reorder the terms: (-15 + 4a)(23 + 7a) = 0 Multiply (-15 + 4a) * (23 + 7a) (-15(23 + 7a) + 4a * (23 + 7a)) = 0 ((23 * -15 + 7a * -15) + 4a * (23 + 7a)) = 0 ((-345 + -105a) + 4a * (23 + 7a)) = 0 (-345 + -105a + (23 * 4a + 7a * 4a)) = 0 (-345 + -105a + (92a + 28a2)) = 0 Combine like terms: -105a + 92a = -13a (-345 + -13a + 28a2) = 0 Solving -345 + -13a + 28a2 = 0 Solving for variable 'a'. Factor a trinomial. (-23 + -7a)(15 + -4a) = 0Subproblem 1
Set the factor '(-23 + -7a)' equal to zero and attempt to solve: Simplifying -23 + -7a = 0 Solving -23 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -7a = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -7a = 0 + 23 -7a = 0 + 23 Combine like terms: 0 + 23 = 23 -7a = 23 Divide each side by '-7'. a = -3.285714286 Simplifying a = -3.285714286Subproblem 2
Set the factor '(15 + -4a)' equal to zero and attempt to solve: Simplifying 15 + -4a = 0 Solving 15 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -4a = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4a = 0 + -15 -4a = 0 + -15 Combine like terms: 0 + -15 = -15 -4a = -15 Divide each side by '-4'. a = 3.75 Simplifying a = 3.75Solution
a = {-3.285714286, 3.75}
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