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Simplifying (10a + 7)(3a + -4) = 0 Reorder the terms: (7 + 10a)(3a + -4) = 0 Reorder the terms: (7 + 10a)(-4 + 3a) = 0 Multiply (7 + 10a) * (-4 + 3a) (7(-4 + 3a) + 10a * (-4 + 3a)) = 0 ((-4 * 7 + 3a * 7) + 10a * (-4 + 3a)) = 0 ((-28 + 21a) + 10a * (-4 + 3a)) = 0 (-28 + 21a + (-4 * 10a + 3a * 10a)) = 0 (-28 + 21a + (-40a + 30a2)) = 0 Combine like terms: 21a + -40a = -19a (-28 + -19a + 30a2) = 0 Solving -28 + -19a + 30a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -10a)(4 + -3a) = 0Subproblem 1
Set the factor '(-7 + -10a)' equal to zero and attempt to solve: Simplifying -7 + -10a = 0 Solving -7 + -10a = 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 + -10a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10a = 0 + 7 -10a = 0 + 7 Combine like terms: 0 + 7 = 7 -10a = 7 Divide each side by '-10'. a = -0.7 Simplifying a = -0.7Subproblem 2
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 = 1.333333333Solution
a = {-0.7, 1.333333333}
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