5z^2-30z=-25

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Solution for 5z^2-30z=-25 equation:


Simplifying
5z2 + -30z = -25

Reorder the terms:
-30z + 5z2 = -25

Solving
-30z + 5z2 = -25

Solving for variable 'z'.

Reorder the terms:
25 + -30z + 5z2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + -30z + 5z2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -6z + z2) = 0

Factor a trinomial.
5((1 + -1z)(5 + -1z)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1

Subproblem 2

Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5

Solution

z = {1, 5}

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