0=-x^2-3x+54

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Solution for 0=-x^2-3x+54 equation:


Simplifying
0 = -1x2 + -3x + 54

Reorder the terms:
0 = 54 + -3x + -1x2

Solving
0 = 54 + -3x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -54 = -54
-54 + 3x + x2 = 54 + -3x + -1x2 + -54 + 3x + x2

Reorder the terms:
-54 + 3x + x2 = 54 + -54 + -3x + 3x + -1x2 + x2

Combine like terms: 54 + -54 = 0
-54 + 3x + x2 = 0 + -3x + 3x + -1x2 + x2
-54 + 3x + x2 = -3x + 3x + -1x2 + x2

Combine like terms: -3x + 3x = 0
-54 + 3x + x2 = 0 + -1x2 + x2
-54 + 3x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-54 + 3x + x2 = 0

Factor a trinomial.
(-9 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-9, 6}

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