(4x+9)(x-6)=8x+18

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Solution for (4x+9)(x-6)=8x+18 equation: 


Simplifying
(4x + 9)(x + -6) = 8x + 18

Reorder the terms:
(9 + 4x)(x + -6) = 8x + 18

Reorder the terms:
(9 + 4x)(-6 + x) = 8x + 18

Multiply (9 + 4x) * (-6 + x)
(9(-6 + x) + 4x * (-6 + x)) = 8x + 18
((-6 * 9 + x * 9) + 4x * (-6 + x)) = 8x + 18
((-54 + 9x) + 4x * (-6 + x)) = 8x + 18
(-54 + 9x + (-6 * 4x + x * 4x)) = 8x + 18
(-54 + 9x + (-24x + 4x2)) = 8x + 18

Combine like terms: 9x + -24x = -15x
(-54 + -15x + 4x2) = 8x + 18

Reorder the terms:
-54 + -15x + 4x2 = 18 + 8x

Solving
-54 + -15x + 4x2 = 18 + 8x

Solving for variable 'x'.

Reorder the terms:
-54 + -18 + -15x + -8x + 4x2 = 18 + 8x + -18 + -8x

Combine like terms: -54 + -18 = -72
-72 + -15x + -8x + 4x2 = 18 + 8x + -18 + -8x

Combine like terms: -15x + -8x = -23x
-72 + -23x + 4x2 = 18 + 8x + -18 + -8x

Reorder the terms:
-72 + -23x + 4x2 = 18 + -18 + 8x + -8x

Combine like terms: 18 + -18 = 0
-72 + -23x + 4x2 = 0 + 8x + -8x
-72 + -23x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-72 + -23x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2.25, 8}

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