4x(x-1)=(2x+3)(x-1)

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Solution for 4x(x-1)=(2x+3)(x-1) equation: 


Simplifying
4x(x + -1) = (2x + 3)(x + -1)

Reorder the terms:
4x(-1 + x) = (2x + 3)(x + -1)
(-1 * 4x + x * 4x) = (2x + 3)(x + -1)
(-4x + 4x2) = (2x + 3)(x + -1)

Reorder the terms:
-4x + 4x2 = (3 + 2x)(x + -1)

Reorder the terms:
-4x + 4x2 = (3 + 2x)(-1 + x)

Multiply (3 + 2x) * (-1 + x)
-4x + 4x2 = (3(-1 + x) + 2x * (-1 + x))
-4x + 4x2 = ((-1 * 3 + x * 3) + 2x * (-1 + x))
-4x + 4x2 = ((-3 + 3x) + 2x * (-1 + x))
-4x + 4x2 = (-3 + 3x + (-1 * 2x + x * 2x))
-4x + 4x2 = (-3 + 3x + (-2x + 2x2))

Combine like terms: 3x + -2x = 1x
-4x + 4x2 = (-3 + 1x + 2x2)

Solving
-4x + 4x2 = -3 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
3 + -4x + -1x + 4x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: -4x + -1x = -5x
3 + -5x + 4x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
3 + -5x + 2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Reorder the terms:
3 + -5x + 2x2 = -3 + 3 + 1x + -1x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
3 + -5x + 2x2 = 0 + 1x + -1x + 2x2 + -2x2
3 + -5x + 2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
3 + -5x + 2x2 = 0 + 2x2 + -2x2
3 + -5x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + -5x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -2x) = 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 '(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
Solution
x = {1, 1.5}

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