5x(x-3)=(4x+9)(x-3)

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Solution for 5x(x-3)=(4x+9)(x-3) equation: 


Simplifying
5x(x + -3) = (4x + 9)(x + -3)

Reorder the terms:
5x(-3 + x) = (4x + 9)(x + -3)
(-3 * 5x + x * 5x) = (4x + 9)(x + -3)
(-15x + 5x2) = (4x + 9)(x + -3)

Reorder the terms:
-15x + 5x2 = (9 + 4x)(x + -3)

Reorder the terms:
-15x + 5x2 = (9 + 4x)(-3 + x)

Multiply (9 + 4x) * (-3 + x)
-15x + 5x2 = (9(-3 + x) + 4x * (-3 + x))
-15x + 5x2 = ((-3 * 9 + x * 9) + 4x * (-3 + x))
-15x + 5x2 = ((-27 + 9x) + 4x * (-3 + x))
-15x + 5x2 = (-27 + 9x + (-3 * 4x + x * 4x))
-15x + 5x2 = (-27 + 9x + (-12x + 4x2))

Combine like terms: 9x + -12x = -3x
-15x + 5x2 = (-27 + -3x + 4x2)

Solving
-15x + 5x2 = -27 + -3x + 4x2

Solving for variable 'x'.

Reorder the terms:
27 + -15x + 3x + 5x2 + -4x2 = -27 + -3x + 4x2 + 27 + 3x + -4x2

Combine like terms: -15x + 3x = -12x
27 + -12x + 5x2 + -4x2 = -27 + -3x + 4x2 + 27 + 3x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
27 + -12x + 1x2 = -27 + -3x + 4x2 + 27 + 3x + -4x2

Reorder the terms:
27 + -12x + 1x2 = -27 + 27 + -3x + 3x + 4x2 + -4x2

Combine like terms: -27 + 27 = 0
27 + -12x + 1x2 = 0 + -3x + 3x + 4x2 + -4x2
27 + -12x + 1x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
27 + -12x + 1x2 = 0 + 4x2 + -4x2
27 + -12x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
27 + -12x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, 9}

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