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Simplifying (4 + z)(5z + -2) = 0 Reorder the terms: (4 + z)(-2 + 5z) = 0 Multiply (4 + z) * (-2 + 5z) (4(-2 + 5z) + z(-2 + 5z)) = 0 ((-2 * 4 + 5z * 4) + z(-2 + 5z)) = 0 ((-8 + 20z) + z(-2 + 5z)) = 0 (-8 + 20z + (-2 * z + 5z * z)) = 0 (-8 + 20z + (-2z + 5z2)) = 0 Combine like terms: 20z + -2z = 18z (-8 + 18z + 5z2) = 0 Solving -8 + 18z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + -1z)(2 + -5z) = 0Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 2
Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Solution
z = {-4, 0.4}
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