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Simplifying 8(3a + -4) + -7a(3a + -4) = 0 Reorder the terms: 8(-4 + 3a) + -7a(3a + -4) = 0 (-4 * 8 + 3a * 8) + -7a(3a + -4) = 0 (-32 + 24a) + -7a(3a + -4) = 0 Reorder the terms: -32 + 24a + -7a(-4 + 3a) = 0 -32 + 24a + (-4 * -7a + 3a * -7a) = 0 -32 + 24a + (28a + -21a2) = 0 Combine like terms: 24a + 28a = 52a -32 + 52a + -21a2 = 0 Solving -32 + 52a + -21a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + 3a)(8 + -7a) = 0Subproblem 1
Set the factor '(-4 + 3a)' equal to zero and attempt to solve: Simplifying -4 + 3a = 0 Solving -4 + 3a = 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 + 3a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3a = 0 + 4 3a = 0 + 4 Combine like terms: 0 + 4 = 4 3a = 4 Divide each side by '3'. a = 1.333333333 Simplifying a = 1.333333333Subproblem 2
Set the factor '(8 + -7a)' equal to zero and attempt to solve: Simplifying 8 + -7a = 0 Solving 8 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7a = 0 + -8 -7a = 0 + -8 Combine like terms: 0 + -8 = -8 -7a = -8 Divide each side by '-7'. a = 1.142857143 Simplifying a = 1.142857143Solution
a = {1.333333333, 1.142857143}
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