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Simplifying (7a + 3)(4a + -7) = 0 Reorder the terms: (3 + 7a)(4a + -7) = 0 Reorder the terms: (3 + 7a)(-7 + 4a) = 0 Multiply (3 + 7a) * (-7 + 4a) (3(-7 + 4a) + 7a * (-7 + 4a)) = 0 ((-7 * 3 + 4a * 3) + 7a * (-7 + 4a)) = 0 ((-21 + 12a) + 7a * (-7 + 4a)) = 0 (-21 + 12a + (-7 * 7a + 4a * 7a)) = 0 (-21 + 12a + (-49a + 28a2)) = 0 Combine like terms: 12a + -49a = -37a (-21 + -37a + 28a2) = 0 Solving -21 + -37a + 28a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -7a)(7 + -4a) = 0Subproblem 1
Set the factor '(-3 + -7a)' equal to zero and attempt to solve: Simplifying -3 + -7a = 0 Solving -3 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -7a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7a = 0 + 3 -7a = 0 + 3 Combine like terms: 0 + 3 = 3 -7a = 3 Divide each side by '-7'. a = -0.4285714286 Simplifying a = -0.4285714286Subproblem 2
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Solution
a = {-0.4285714286, 1.75}
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