4x(x-9)=(3x+8)(x-9)

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Solution for 4x(x-9)=(3x+8)(x-9) equation: 


Simplifying
4x(x + -9) = (3x + 8)(x + -9)

Reorder the terms:
4x(-9 + x) = (3x + 8)(x + -9)
(-9 * 4x + x * 4x) = (3x + 8)(x + -9)
(-36x + 4x2) = (3x + 8)(x + -9)

Reorder the terms:
-36x + 4x2 = (8 + 3x)(x + -9)

Reorder the terms:
-36x + 4x2 = (8 + 3x)(-9 + x)

Multiply (8 + 3x) * (-9 + x)
-36x + 4x2 = (8(-9 + x) + 3x * (-9 + x))
-36x + 4x2 = ((-9 * 8 + x * 8) + 3x * (-9 + x))
-36x + 4x2 = ((-72 + 8x) + 3x * (-9 + x))
-36x + 4x2 = (-72 + 8x + (-9 * 3x + x * 3x))
-36x + 4x2 = (-72 + 8x + (-27x + 3x2))

Combine like terms: 8x + -27x = -19x
-36x + 4x2 = (-72 + -19x + 3x2)

Solving
-36x + 4x2 = -72 + -19x + 3x2

Solving for variable 'x'.

Reorder the terms:
72 + -36x + 19x + 4x2 + -3x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Combine like terms: -36x + 19x = -17x
72 + -17x + 4x2 + -3x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
72 + -17x + 1x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Reorder the terms:
72 + -17x + 1x2 = -72 + 72 + -19x + 19x + 3x2 + -3x2

Combine like terms: -72 + 72 = 0
72 + -17x + 1x2 = 0 + -19x + 19x + 3x2 + -3x2
72 + -17x + 1x2 = -19x + 19x + 3x2 + -3x2

Combine like terms: -19x + 19x = 0
72 + -17x + 1x2 = 0 + 3x2 + -3x2
72 + -17x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
72 + -17x + 1x2 = 0

Factor a trinomial.
(8 + -1x)(9 + -1x) = 0


Subproblem 1
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

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 = {8, 9}

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