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Simplifying (2a + -3)(5a + 4) = 0 Reorder the terms: (-3 + 2a)(5a + 4) = 0 Reorder the terms: (-3 + 2a)(4 + 5a) = 0 Multiply (-3 + 2a) * (4 + 5a) (-3(4 + 5a) + 2a * (4 + 5a)) = 0 ((4 * -3 + 5a * -3) + 2a * (4 + 5a)) = 0 ((-12 + -15a) + 2a * (4 + 5a)) = 0 (-12 + -15a + (4 * 2a + 5a * 2a)) = 0 (-12 + -15a + (8a + 10a2)) = 0 Combine like terms: -15a + 8a = -7a (-12 + -7a + 10a2) = 0 Solving -12 + -7a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -5a)(3 + -2a) = 0Subproblem 1
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 = -0.8Subproblem 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 = {-0.8, 1.5}
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