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Simplifying 2z(20z + 141) = 135 Reorder the terms: 2z(141 + 20z) = 135 (141 * 2z + 20z * 2z) = 135 (282z + 40z2) = 135 Solving 282z + 40z2 = 135 Solving for variable 'z'. Reorder the terms: -135 + 282z + 40z2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + 282z + 40z2 = 0 Factor a trinomial. (-15 + -2z)(9 + -20z) = 0Subproblem 1
Set the factor '(-15 + -2z)' equal to zero and attempt to solve: Simplifying -15 + -2z = 0 Solving -15 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2z = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2z = 0 + 15 -2z = 0 + 15 Combine like terms: 0 + 15 = 15 -2z = 15 Divide each side by '-2'. z = -7.5 Simplifying z = -7.5Subproblem 2
Set the factor '(9 + -20z)' equal to zero and attempt to solve: Simplifying 9 + -20z = 0 Solving 9 + -20z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -20z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -20z = 0 + -9 -20z = 0 + -9 Combine like terms: 0 + -9 = -9 -20z = -9 Divide each side by '-20'. z = 0.45 Simplifying z = 0.45Solution
z = {-7.5, 0.45}
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