9z+7z^2=10

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Solution for 9z+7z^2=10 equation:


Simplifying
9z + 7z2 = 10

Solving
9z + 7z2 = 10

Solving for variable 'z'.

Reorder the terms:
-10 + 9z + 7z2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 9z + 7z2 = 0

Factor a trinomial.
(-2 + -1z)(5 + -7z) = 0

Subproblem 1

Set the factor '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2

Subproblem 2

Set the factor '(5 + -7z)' equal to zero and attempt to solve: Simplifying 5 + -7z = 0 Solving 5 + -7z = 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 + -7z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7z = 0 + -5 -7z = 0 + -5 Combine like terms: 0 + -5 = -5 -7z = -5 Divide each side by '-7'. z = 0.7142857143 Simplifying z = 0.7142857143

Solution

z = {-2, 0.7142857143}

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