5x(x-9)=(4x+6)(x-9)

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Solution for 5x(x-9)=(4x+6)(x-9) equation: 


Simplifying
5x(x + -9) = (4x + 6)(x + -9)

Reorder the terms:
5x(-9 + x) = (4x + 6)(x + -9)
(-9 * 5x + x * 5x) = (4x + 6)(x + -9)
(-45x + 5x2) = (4x + 6)(x + -9)

Reorder the terms:
-45x + 5x2 = (6 + 4x)(x + -9)

Reorder the terms:
-45x + 5x2 = (6 + 4x)(-9 + x)

Multiply (6 + 4x) * (-9 + x)
-45x + 5x2 = (6(-9 + x) + 4x * (-9 + x))
-45x + 5x2 = ((-9 * 6 + x * 6) + 4x * (-9 + x))
-45x + 5x2 = ((-54 + 6x) + 4x * (-9 + x))
-45x + 5x2 = (-54 + 6x + (-9 * 4x + x * 4x))
-45x + 5x2 = (-54 + 6x + (-36x + 4x2))

Combine like terms: 6x + -36x = -30x
-45x + 5x2 = (-54 + -30x + 4x2)

Solving
-45x + 5x2 = -54 + -30x + 4x2

Solving for variable 'x'.

Reorder the terms:
54 + -45x + 30x + 5x2 + -4x2 = -54 + -30x + 4x2 + 54 + 30x + -4x2

Combine like terms: -45x + 30x = -15x
54 + -15x + 5x2 + -4x2 = -54 + -30x + 4x2 + 54 + 30x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
54 + -15x + 1x2 = -54 + -30x + 4x2 + 54 + 30x + -4x2

Reorder the terms:
54 + -15x + 1x2 = -54 + 54 + -30x + 30x + 4x2 + -4x2

Combine like terms: -54 + 54 = 0
54 + -15x + 1x2 = 0 + -30x + 30x + 4x2 + -4x2
54 + -15x + 1x2 = -30x + 30x + 4x2 + -4x2

Combine like terms: -30x + 30x = 0
54 + -15x + 1x2 = 0 + 4x2 + -4x2
54 + -15x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
54 + -15x + 1x2 = 0

Factor a trinomial.
(6 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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 = {6, 9}

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