2x^2-7x+6=(x-2)(x-2)

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Solution for 2x^2-7x+6=(x-2)(x-2) equation: 


Simplifying
2x2 + -7x + 6 = (x + -2)(x + -2)

Reorder the terms:
6 + -7x + 2x2 = (x + -2)(x + -2)

Reorder the terms:
6 + -7x + 2x2 = (-2 + x)(x + -2)

Reorder the terms:
6 + -7x + 2x2 = (-2 + x)(-2 + x)

Multiply (-2 + x) * (-2 + x)
6 + -7x + 2x2 = (-2(-2 + x) + x(-2 + x))
6 + -7x + 2x2 = ((-2 * -2 + x * -2) + x(-2 + x))
6 + -7x + 2x2 = ((4 + -2x) + x(-2 + x))
6 + -7x + 2x2 = (4 + -2x + (-2 * x + x * x))
6 + -7x + 2x2 = (4 + -2x + (-2x + x2))

Combine like terms: -2x + -2x = -4x
6 + -7x + 2x2 = (4 + -4x + x2)

Solving
6 + -7x + 2x2 = 4 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
6 + -4 + -7x + 4x + 2x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Combine like terms: 6 + -4 = 2
2 + -7x + 4x + 2x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

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

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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