(z-4)(z+7)=0

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Solution for (z-4)(z+7)=0 equation:


Simplifying
(z + -4)(z + 7) = 0

Reorder the terms:
(-4 + z)(z + 7) = 0

Reorder the terms:
(-4 + z)(7 + z) = 0

Multiply (-4 + z) * (7 + z)
(-4(7 + z) + z(7 + z)) = 0
((7 * -4 + z * -4) + z(7 + z)) = 0
((-28 + -4z) + z(7 + z)) = 0
(-28 + -4z + (7 * z + z * z)) = 0
(-28 + -4z + (7z + z2)) = 0

Combine like terms: -4z + 7z = 3z
(-28 + 3z + z2) = 0

Solving
-28 + 3z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(4 + -1z) = 0

Subproblem 1

Set the factor '(-7 + -1z)' equal to zero and attempt to solve: Simplifying -7 + -1z = 0 Solving -7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1z = 0 + 7 -1z = 0 + 7 Combine like terms: 0 + 7 = 7 -1z = 7 Divide each side by '-1'. z = -7 Simplifying z = -7

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 = {-7, 4}

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