(4x+9)(x-6)=12x+27

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Solution for (4x+9)(x-6)=12x+27 equation: 


Simplifying
(4x + 9)(x + -6) = 12x + 27

Reorder the terms:
(9 + 4x)(x + -6) = 12x + 27

Reorder the terms:
(9 + 4x)(-6 + x) = 12x + 27

Multiply (9 + 4x) * (-6 + x)
(9(-6 + x) + 4x * (-6 + x)) = 12x + 27
((-6 * 9 + x * 9) + 4x * (-6 + x)) = 12x + 27
((-54 + 9x) + 4x * (-6 + x)) = 12x + 27
(-54 + 9x + (-6 * 4x + x * 4x)) = 12x + 27
(-54 + 9x + (-24x + 4x2)) = 12x + 27

Combine like terms: 9x + -24x = -15x
(-54 + -15x + 4x2) = 12x + 27

Reorder the terms:
-54 + -15x + 4x2 = 27 + 12x

Solving
-54 + -15x + 4x2 = 27 + 12x

Solving for variable 'x'.

Reorder the terms:
-54 + -27 + -15x + -12x + 4x2 = 27 + 12x + -27 + -12x

Combine like terms: -54 + -27 = -81
-81 + -15x + -12x + 4x2 = 27 + 12x + -27 + -12x

Combine like terms: -15x + -12x = -27x
-81 + -27x + 4x2 = 27 + 12x + -27 + -12x

Reorder the terms:
-81 + -27x + 4x2 = 27 + -27 + 12x + -12x

Combine like terms: 27 + -27 = 0
-81 + -27x + 4x2 = 0 + 12x + -12x
-81 + -27x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-81 + -27x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(9 + -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 '(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 = {-2.25, 9}

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