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Simplifying z(2z + 7) = 4 Reorder the terms: z(7 + 2z) = 4 (7 * z + 2z * z) = 4 (7z + 2z2) = 4 Solving 7z + 2z2 = 4 Solving for variable 'z'. Reorder the terms: -4 + 7z + 2z2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 7z + 2z2 = 0 Factor a trinomial. (-4 + -1z)(1 + -2z) = 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 '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 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 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5Solution
z = {-4, 0.5}
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