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Simplifying (7z + -1a)(3z + 2a) = 0 Reorder the terms: (-1a + 7z)(3z + 2a) = 0 Reorder the terms: (-1a + 7z)(2a + 3z) = 0 Multiply (-1a + 7z) * (2a + 3z) (-1a * (2a + 3z) + 7z * (2a + 3z)) = 0 ((2a * -1a + 3z * -1a) + 7z * (2a + 3z)) = 0 Reorder the terms: ((-3az + -2a2) + 7z * (2a + 3z)) = 0 ((-3az + -2a2) + 7z * (2a + 3z)) = 0 (-3az + -2a2 + (2a * 7z + 3z * 7z)) = 0 (-3az + -2a2 + (14az + 21z2)) = 0 Reorder the terms: (-3az + 14az + -2a2 + 21z2) = 0 Combine like terms: -3az + 14az = 11az (11az + -2a2 + 21z2) = 0 Solving 11az + -2a2 + 21z2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -3z)(a + -7z) = 0Subproblem 1
Set the factor '(-2a + -3z)' equal to zero and attempt to solve: Simplifying -2a + -3z = 0 Solving -2a + -3z = 0 Move all terms containing a to the left, all other terms to the right. Add '3z' to each side of the equation. -2a + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 -2a + 0 = 0 + 3z -2a = 0 + 3z Remove the zero: -2a = 3z Divide each side by '-2'. a = -1.5z Simplifying a = -1.5zSubproblem 2
Set the factor '(a + -7z)' equal to zero and attempt to solve: Simplifying a + -7z = 0 Solving a + -7z = 0 Move all terms containing a to the left, all other terms to the right. Add '7z' to each side of the equation. a + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 a + 0 = 0 + 7z a = 0 + 7z Remove the zero: a = 7z Simplifying a = 7zSolution
a = {-1.5z, 7z}
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