x^2-x-30=9x-54

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Solution for x^2-x-30=9x-54 equation:


Simplifying
x2 + -1x + -30 = 9x + -54

Reorder the terms:
-30 + -1x + x2 = 9x + -54

Reorder the terms:
-30 + -1x + x2 = -54 + 9x

Solving
-30 + -1x + x2 = -54 + 9x

Solving for variable 'x'.

Reorder the terms:
-30 + 54 + -1x + -9x + x2 = -54 + 9x + 54 + -9x

Combine like terms: -30 + 54 = 24
24 + -1x + -9x + x2 = -54 + 9x + 54 + -9x

Combine like terms: -1x + -9x = -10x
24 + -10x + x2 = -54 + 9x + 54 + -9x

Reorder the terms:
24 + -10x + x2 = -54 + 54 + 9x + -9x

Combine like terms: -54 + 54 = 0
24 + -10x + x2 = 0 + 9x + -9x
24 + -10x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
24 + -10x + x2 = 0

Factor a trinomial.
(4 + -1x)(6 + -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 '(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 = {4, 6}

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