x^2-2x=4x+27

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Solution for x^2-2x=4x+27 equation:


Simplifying
x2 + -2x = 4x + 27

Reorder the terms:
-2x + x2 = 4x + 27

Reorder the terms:
-2x + x2 = 27 + 4x

Solving
-2x + x2 = 27 + 4x

Solving for variable 'x'.

Reorder the terms:
-27 + -2x + -4x + x2 = 27 + 4x + -27 + -4x

Combine like terms: -2x + -4x = -6x
-27 + -6x + x2 = 27 + 4x + -27 + -4x

Reorder the terms:
-27 + -6x + x2 = 27 + -27 + 4x + -4x

Combine like terms: 27 + -27 = 0
-27 + -6x + x2 = 0 + 4x + -4x
-27 + -6x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-27 + -6x + x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -1x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

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

Solution

x = {-3, 9}

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