7-2x=(x-2)(x-2)

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Solution for 7-2x=(x-2)(x-2) equation: 


Simplifying
7 + -2x = (x + -2)(x + -2)

Reorder the terms:
7 + -2x = (-2 + x)(x + -2)

Reorder the terms:
7 + -2x = (-2 + x)(-2 + x)

Multiply (-2 + x) * (-2 + x)
7 + -2x = (-2(-2 + x) + x(-2 + x))
7 + -2x = ((-2 * -2 + x * -2) + x(-2 + x))
7 + -2x = ((4 + -2x) + x(-2 + x))
7 + -2x = (4 + -2x + (-2 * x + x * x))
7 + -2x = (4 + -2x + (-2x + x2))

Combine like terms: -2x + -2x = -4x
7 + -2x = (4 + -4x + x2)

Solving
7 + -2x = 4 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -4 + -2x + 4x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Combine like terms: 7 + -4 = 3
3 + -2x + 4x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

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

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

Combine like terms: 4 + -4 = 0
3 + 2x + -1x2 = 0 + -4x + 4x + x2 + -1x2
3 + 2x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
3 + 2x + -1x2 = 0 + x2 + -1x2
3 + 2x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(3 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}

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