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Simplifying (3 + -4a)(3 + -7a) = 0 Multiply (3 + -4a) * (3 + -7a) (3(3 + -7a) + -4a * (3 + -7a)) = 0 ((3 * 3 + -7a * 3) + -4a * (3 + -7a)) = 0 ((9 + -21a) + -4a * (3 + -7a)) = 0 (9 + -21a + (3 * -4a + -7a * -4a)) = 0 (9 + -21a + (-12a + 28a2)) = 0 Combine like terms: -21a + -12a = -33a (9 + -33a + 28a2) = 0 Solving 9 + -33a + 28a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -7a)(3 + -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 '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {0.4285714286, 0.75}
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