(z-5)(z+4)=70

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Solution for (z-5)(z+4)=70 equation:


Simplifying
(z + -5)(z + 4) = 70

Reorder the terms:
(-5 + z)(z + 4) = 70

Reorder the terms:
(-5 + z)(4 + z) = 70

Multiply (-5 + z) * (4 + z)
(-5(4 + z) + z(4 + z)) = 70
((4 * -5 + z * -5) + z(4 + z)) = 70
((-20 + -5z) + z(4 + z)) = 70
(-20 + -5z + (4 * z + z * z)) = 70
(-20 + -5z + (4z + z2)) = 70

Combine like terms: -5z + 4z = -1z
(-20 + -1z + z2) = 70

Solving
-20 + -1z + z2 = 70

Solving for variable 'z'.

Reorder the terms:
-20 + -70 + -1z + z2 = 70 + -70

Combine like terms: -20 + -70 = -90
-90 + -1z + z2 = 70 + -70

Combine like terms: 70 + -70 = 0
-90 + -1z + z2 = 0

Factor a trinomial.
(-9 + -1z)(10 + -1z) = 0

Subproblem 1

Set the factor '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 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 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9

Subproblem 2

Set the factor '(10 + -1z)' equal to zero and attempt to solve: Simplifying 10 + -1z = 0 Solving 10 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1z = 0 + -10 -1z = 0 + -10 Combine like terms: 0 + -10 = -10 -1z = -10 Divide each side by '-1'. z = 10 Simplifying z = 10

Solution

z = {-9, 10}

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