240=-x^2+32x+9

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Solution for 240=-x^2+32x+9 equation:


Simplifying
240 = -1x2 + 32x + 9

Reorder the terms:
240 = 9 + 32x + -1x2

Solving
240 = 9 + 32x + -1x2

Solving for variable 'x'.

Combine like terms: 240 + -9 = 231
231 + -32x + x2 = 9 + 32x + -1x2 + -9 + -32x + x2

Reorder the terms:
231 + -32x + x2 = 9 + -9 + 32x + -32x + -1x2 + x2

Combine like terms: 9 + -9 = 0
231 + -32x + x2 = 0 + 32x + -32x + -1x2 + x2
231 + -32x + x2 = 32x + -32x + -1x2 + x2

Combine like terms: 32x + -32x = 0
231 + -32x + x2 = 0 + -1x2 + x2
231 + -32x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
231 + -32x + x2 = 0

Factor a trinomial.
(11 + -1x)(21 + -1x) = 0

Subproblem 1

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Subproblem 2

Set the factor '(21 + -1x)' equal to zero and attempt to solve: Simplifying 21 + -1x = 0 Solving 21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1x = 0 + -21 -1x = 0 + -21 Combine like terms: 0 + -21 = -21 -1x = -21 Divide each side by '-1'. x = 21 Simplifying x = 21

Solution

x = {11, 21}

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