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Simplifying 5z(2z + 3) = 2z + 3 Reorder the terms: 5z(3 + 2z) = 2z + 3 (3 * 5z + 2z * 5z) = 2z + 3 (15z + 10z2) = 2z + 3 Reorder the terms: 15z + 10z2 = 3 + 2z Solving 15z + 10z2 = 3 + 2z Solving for variable 'z'. Reorder the terms: -3 + 15z + -2z + 10z2 = 3 + 2z + -3 + -2z Combine like terms: 15z + -2z = 13z -3 + 13z + 10z2 = 3 + 2z + -3 + -2z Reorder the terms: -3 + 13z + 10z2 = 3 + -3 + 2z + -2z Combine like terms: 3 + -3 = 0 -3 + 13z + 10z2 = 0 + 2z + -2z -3 + 13z + 10z2 = 2z + -2z Combine like terms: 2z + -2z = 0 -3 + 13z + 10z2 = 0 Factor a trinomial. (-3 + -2z)(1 + -5z) = 0Subproblem 1
Set the factor '(-3 + -2z)' equal to zero and attempt to solve: Simplifying -3 + -2z = 0 Solving -3 + -2z = 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 + -2z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2z = 0 + 3 -2z = 0 + 3 Combine like terms: 0 + 3 = 3 -2z = 3 Divide each side by '-2'. z = -1.5 Simplifying z = -1.5Subproblem 2
Set the factor '(1 + -5z)' equal to zero and attempt to solve: Simplifying 1 + -5z = 0 Solving 1 + -5z = 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 + -5z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5z = 0 + -1 -5z = 0 + -1 Combine like terms: 0 + -1 = -1 -5z = -1 Divide each side by '-5'. z = 0.2 Simplifying z = 0.2Solution
z = {-1.5, 0.2}
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