4x^2-x=2x+27

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


Simplifying
4x2 + -1x = 2x + 27

Reorder the terms:
-1x + 4x2 = 2x + 27

Reorder the terms:
-1x + 4x2 = 27 + 2x

Solving
-1x + 4x2 = 27 + 2x

Solving for variable 'x'.

Reorder the terms:
-27 + -1x + -2x + 4x2 = 27 + 2x + -27 + -2x

Combine like terms: -1x + -2x = -3x
-27 + -3x + 4x2 = 27 + 2x + -27 + -2x

Reorder the terms:
-27 + -3x + 4x2 = 27 + -27 + 2x + -2x

Combine like terms: 27 + -27 = 0
-27 + -3x + 4x2 = 0 + 2x + -2x
-27 + -3x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-27 + -3x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 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 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
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
Solution
x = {-2.25, 3}

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