x^2-21x+80=180

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Solution for x^2-21x+80=180 equation:


Simplifying
x2 + -21x + 80 = 180

Reorder the terms:
80 + -21x + x2 = 180

Solving
80 + -21x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
80 + -180 + -21x + x2 = 180 + -180

Combine like terms: 80 + -180 = -100
-100 + -21x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-100 + -21x + x2 = 0

Factor a trinomial.
(-4 + -1x)(25 + -1x) = 0

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25

Solution

x = {-4, 25}

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