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Simplifying (5z + -7)(4z + 1) = 0 Reorder the terms: (-7 + 5z)(4z + 1) = 0 Reorder the terms: (-7 + 5z)(1 + 4z) = 0 Multiply (-7 + 5z) * (1 + 4z) (-7(1 + 4z) + 5z * (1 + 4z)) = 0 ((1 * -7 + 4z * -7) + 5z * (1 + 4z)) = 0 ((-7 + -28z) + 5z * (1 + 4z)) = 0 (-7 + -28z + (1 * 5z + 4z * 5z)) = 0 (-7 + -28z + (5z + 20z2)) = 0 Combine like terms: -28z + 5z = -23z (-7 + -23z + 20z2) = 0 Solving -7 + -23z + 20z2 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -4z)(7 + -5z) = 0Subproblem 1
Set the factor '(-1 + -4z)' equal to zero and attempt to solve: Simplifying -1 + -4z = 0 Solving -1 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4z = 0 + 1 -4z = 0 + 1 Combine like terms: 0 + 1 = 1 -4z = 1 Divide each side by '-4'. z = -0.25 Simplifying z = -0.25Subproblem 2
Set the factor '(7 + -5z)' equal to zero and attempt to solve: Simplifying 7 + -5z = 0 Solving 7 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5z = 0 + -7 -5z = 0 + -7 Combine like terms: 0 + -7 = -7 -5z = -7 Divide each side by '-5'. z = 1.4 Simplifying z = 1.4Solution
z = {-0.25, 1.4}
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