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

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


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

Reorder the terms:
4x(-3 + x) = (2x + 3)(x + -3)
(-3 * 4x + x * 4x) = (2x + 3)(x + -3)
(-12x + 4x2) = (2x + 3)(x + -3)

Reorder the terms:
-12x + 4x2 = (3 + 2x)(x + -3)

Reorder the terms:
-12x + 4x2 = (3 + 2x)(-3 + x)

Multiply (3 + 2x) * (-3 + x)
-12x + 4x2 = (3(-3 + x) + 2x * (-3 + x))
-12x + 4x2 = ((-3 * 3 + x * 3) + 2x * (-3 + x))
-12x + 4x2 = ((-9 + 3x) + 2x * (-3 + x))
-12x + 4x2 = (-9 + 3x + (-3 * 2x + x * 2x))
-12x + 4x2 = (-9 + 3x + (-6x + 2x2))

Combine like terms: 3x + -6x = -3x
-12x + 4x2 = (-9 + -3x + 2x2)

Solving
-12x + 4x2 = -9 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
9 + -12x + 3x + 4x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2

Combine like terms: -12x + 3x = -9x
9 + -9x + 4x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
9 + -9x + 2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2

Reorder the terms:
9 + -9x + 2x2 = -9 + 9 + -3x + 3x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
9 + -9x + 2x2 = 0 + -3x + 3x + 2x2 + -2x2
9 + -9x + 2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
9 + -9x + 2x2 = 0 + 2x2 + -2x2
9 + -9x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
9 + -9x + 2x2 = 0

Factor a trinomial.
(3 + -2x)(3 + -1x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
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
Solution
x = {1.5, 3}

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