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

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


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

Multiply (2 + -3x) * (2 + -3x)
(2(2 + -3x) + -3x * (2 + -3x)) = (x + 1)(x + 1)
((2 * 2 + -3x * 2) + -3x * (2 + -3x)) = (x + 1)(x + 1)
((4 + -6x) + -3x * (2 + -3x)) = (x + 1)(x + 1)
(4 + -6x + (2 * -3x + -3x * -3x)) = (x + 1)(x + 1)
(4 + -6x + (-6x + 9x2)) = (x + 1)(x + 1)

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = (x + 1)(x + 1)

Reorder the terms:
4 + -12x + 9x2 = (1 + x)(x + 1)

Reorder the terms:
4 + -12x + 9x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
4 + -12x + 9x2 = (1(1 + x) + x(1 + x))
4 + -12x + 9x2 = ((1 * 1 + x * 1) + x(1 + x))
4 + -12x + 9x2 = ((1 + 1x) + x(1 + x))
4 + -12x + 9x2 = (1 + 1x + (1 * x + x * x))
4 + -12x + 9x2 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
4 + -12x + 9x2 = (1 + 2x + x2)

Solving
4 + -12x + 9x2 = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
4 + -1 + -12x + -2x + 9x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 4 + -1 = 3
3 + -12x + -2x + 9x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -12x + -2x = -14x
3 + -14x + 9x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 9x2 + -1x2 = 8x2
3 + -14x + 8x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
3 + -14x + 8x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
3 + -14x + 8x2 = 0 + 2x + -2x + x2 + -1x2
3 + -14x + 8x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
3 + -14x + 8x2 = 0 + x2 + -1x2
3 + -14x + 8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -14x + 8x2 = 0

Factor a trinomial.
(1 + -4x)(3 + -2x) = 0


Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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 = {0.25, 1.5}

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