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Simplifying (2a + -3)(7a + -4) = 0 Reorder the terms: (-3 + 2a)(7a + -4) = 0 Reorder the terms: (-3 + 2a)(-4 + 7a) = 0 Multiply (-3 + 2a) * (-4 + 7a) (-3(-4 + 7a) + 2a * (-4 + 7a)) = 0 ((-4 * -3 + 7a * -3) + 2a * (-4 + 7a)) = 0 ((12 + -21a) + 2a * (-4 + 7a)) = 0 (12 + -21a + (-4 * 2a + 7a * 2a)) = 0 (12 + -21a + (-8a + 14a2)) = 0 Combine like terms: -21a + -8a = -29a (12 + -29a + 14a2) = 0 Solving 12 + -29a + 14a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + -7a)(3 + -2a) = 0Subproblem 1
Set the factor '(4 + -7a)' equal to zero and attempt to solve: Simplifying 4 + -7a = 0 Solving 4 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7a = 0 + -4 -7a = 0 + -4 Combine like terms: 0 + -4 = -4 -7a = -4 Divide each side by '-7'. a = 0.5714285714 Simplifying a = 0.5714285714Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {0.5714285714, 1.5}
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