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Simplifying (-5a + 4)(-7a + 4) = 0 Reorder the terms: (4 + -5a)(-7a + 4) = 0 Reorder the terms: (4 + -5a)(4 + -7a) = 0 Multiply (4 + -5a) * (4 + -7a) (4(4 + -7a) + -5a * (4 + -7a)) = 0 ((4 * 4 + -7a * 4) + -5a * (4 + -7a)) = 0 ((16 + -28a) + -5a * (4 + -7a)) = 0 (16 + -28a + (4 * -5a + -7a * -5a)) = 0 (16 + -28a + (-20a + 35a2)) = 0 Combine like terms: -28a + -20a = -48a (16 + -48a + 35a2) = 0 Solving 16 + -48a + 35a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + -7a)(4 + -5a) = 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 '(4 + -5a)' equal to zero and attempt to solve: Simplifying 4 + -5a = 0 Solving 4 + -5a = 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 + -5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5a = 0 + -4 -5a = 0 + -4 Combine like terms: 0 + -4 = -4 -5a = -4 Divide each side by '-5'. a = 0.8 Simplifying a = 0.8Solution
a = {0.5714285714, 0.8}
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