77z^4-100z^3+32z^2=0

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Solution for 77z^4-100z^3+32z^2=0 equation:


Simplifying
77z4 + -100z3 + 32z2 = 0

Reorder the terms:
32z2 + -100z3 + 77z4 = 0

Solving
32z2 + -100z3 + 77z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(32 + -100z + 77z2) = 0

Factor a trinomial.
z2((4 + -7z)(8 + -11z)) = 0

Subproblem 1

Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}

Subproblem 2

Set the factor '(4 + -7z)' equal to zero and attempt to solve: Simplifying 4 + -7z = 0 Solving 4 + -7z = 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 + -7z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7z = 0 + -4 -7z = 0 + -4 Combine like terms: 0 + -4 = -4 -7z = -4 Divide each side by '-7'. z = 0.5714285714 Simplifying z = 0.5714285714

Subproblem 3

Set the factor '(8 + -11z)' equal to zero and attempt to solve: Simplifying 8 + -11z = 0 Solving 8 + -11z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -11z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11z = 0 + -8 -11z = 0 + -8 Combine like terms: 0 + -8 = -8 -11z = -8 Divide each side by '-11'. z = 0.7272727273 Simplifying z = 0.7272727273

Solution

z = {0, 0.5714285714, 0.7272727273}

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