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Simplifying (z + -10)(4z + 3) = 0 Reorder the terms: (-10 + z)(4z + 3) = 0 Reorder the terms: (-10 + z)(3 + 4z) = 0 Multiply (-10 + z) * (3 + 4z) (-10(3 + 4z) + z(3 + 4z)) = 0 ((3 * -10 + 4z * -10) + z(3 + 4z)) = 0 ((-30 + -40z) + z(3 + 4z)) = 0 (-30 + -40z + (3 * z + 4z * z)) = 0 (-30 + -40z + (3z + 4z2)) = 0 Combine like terms: -40z + 3z = -37z (-30 + -37z + 4z2) = 0 Solving -30 + -37z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + -4z)(10 + -1z) = 0Subproblem 1
Set the factor '(-3 + -4z)' equal to zero and attempt to solve: Simplifying -3 + -4z = 0 Solving -3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4z = 0 + 3 -4z = 0 + 3 Combine like terms: 0 + 3 = 3 -4z = 3 Divide each side by '-4'. z = -0.75 Simplifying z = -0.75Subproblem 2
Set the factor '(10 + -1z)' equal to zero and attempt to solve: Simplifying 10 + -1z = 0 Solving 10 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1z = 0 + -10 -1z = 0 + -10 Combine like terms: 0 + -10 = -10 -1z = -10 Divide each side by '-1'. z = 10 Simplifying z = 10Solution
z = {-0.75, 10}
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