(x-9)(2x+3)=(x-9)(x+4)

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Solution for (x-9)(2x+3)=(x-9)(x+4) equation: 


Simplifying
(x + -9)(2x + 3) = (x + -9)(x + 4)

Reorder the terms:
(-9 + x)(2x + 3) = (x + -9)(x + 4)

Reorder the terms:
(-9 + x)(3 + 2x) = (x + -9)(x + 4)

Multiply (-9 + x) * (3 + 2x)
(-9(3 + 2x) + x(3 + 2x)) = (x + -9)(x + 4)
((3 * -9 + 2x * -9) + x(3 + 2x)) = (x + -9)(x + 4)
((-27 + -18x) + x(3 + 2x)) = (x + -9)(x + 4)
(-27 + -18x + (3 * x + 2x * x)) = (x + -9)(x + 4)
(-27 + -18x + (3x + 2x2)) = (x + -9)(x + 4)

Combine like terms: -18x + 3x = -15x
(-27 + -15x + 2x2) = (x + -9)(x + 4)

Reorder the terms:
-27 + -15x + 2x2 = (-9 + x)(x + 4)

Reorder the terms:
-27 + -15x + 2x2 = (-9 + x)(4 + x)

Multiply (-9 + x) * (4 + x)
-27 + -15x + 2x2 = (-9(4 + x) + x(4 + x))
-27 + -15x + 2x2 = ((4 * -9 + x * -9) + x(4 + x))
-27 + -15x + 2x2 = ((-36 + -9x) + x(4 + x))
-27 + -15x + 2x2 = (-36 + -9x + (4 * x + x * x))
-27 + -15x + 2x2 = (-36 + -9x + (4x + x2))

Combine like terms: -9x + 4x = -5x
-27 + -15x + 2x2 = (-36 + -5x + x2)

Solving
-27 + -15x + 2x2 = -36 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
-27 + 36 + -15x + 5x + 2x2 + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Combine like terms: -27 + 36 = 9
9 + -15x + 5x + 2x2 + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Combine like terms: -15x + 5x = -10x
9 + -10x + 2x2 + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
9 + -10x + 1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Reorder the terms:
9 + -10x + 1x2 = -36 + 36 + -5x + 5x + x2 + -1x2

Combine like terms: -36 + 36 = 0
9 + -10x + 1x2 = 0 + -5x + 5x + x2 + -1x2
9 + -10x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
9 + -10x + 1x2 = 0 + x2 + -1x2
9 + -10x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + -10x + 1x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {1, 9}

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