z^2+4=8+3z

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Solution for z^2+4=8+3z equation:


Simplifying
z2 + 4 = 8 + 3z

Reorder the terms:
4 + z2 = 8 + 3z

Solving
4 + z2 = 8 + 3z

Solving for variable 'z'.

Reorder the terms:
4 + -8 + -3z + z2 = 8 + 3z + -8 + -3z

Combine like terms: 4 + -8 = -4
-4 + -3z + z2 = 8 + 3z + -8 + -3z

Reorder the terms:
-4 + -3z + z2 = 8 + -8 + 3z + -3z

Combine like terms: 8 + -8 = 0
-4 + -3z + z2 = 0 + 3z + -3z
-4 + -3z + z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
-4 + -3z + z2 = 0

Factor a trinomial.
(-1 + -1z)(4 + -1z) = 0

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 '(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 = 4

Solution

z = {-1, 4}

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