(2x+9)(x-6)=6x+27

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Solution for (2x+9)(x-6)=6x+27 equation: 


Simplifying
(2x + 9)(x + -6) = 6x + 27

Reorder the terms:
(9 + 2x)(x + -6) = 6x + 27

Reorder the terms:
(9 + 2x)(-6 + x) = 6x + 27

Multiply (9 + 2x) * (-6 + x)
(9(-6 + x) + 2x * (-6 + x)) = 6x + 27
((-6 * 9 + x * 9) + 2x * (-6 + x)) = 6x + 27
((-54 + 9x) + 2x * (-6 + x)) = 6x + 27
(-54 + 9x + (-6 * 2x + x * 2x)) = 6x + 27
(-54 + 9x + (-12x + 2x2)) = 6x + 27

Combine like terms: 9x + -12x = -3x
(-54 + -3x + 2x2) = 6x + 27

Reorder the terms:
-54 + -3x + 2x2 = 27 + 6x

Solving
-54 + -3x + 2x2 = 27 + 6x

Solving for variable 'x'.

Reorder the terms:
-54 + -27 + -3x + -6x + 2x2 = 27 + 6x + -27 + -6x

Combine like terms: -54 + -27 = -81
-81 + -3x + -6x + 2x2 = 27 + 6x + -27 + -6x

Combine like terms: -3x + -6x = -9x
-81 + -9x + 2x2 = 27 + 6x + -27 + -6x

Reorder the terms:
-81 + -9x + 2x2 = 27 + -27 + 6x + -6x

Combine like terms: 27 + -27 = 0
-81 + -9x + 2x2 = 0 + 6x + -6x
-81 + -9x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-81 + -9x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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 = {-4.5, 9}

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