4x-3=x^2-4x+4

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Solution for 4x-3=x^2-4x+4 equation: 


Simplifying
4x + -3 = x2 + -4x + 4

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 4x + 4x = 8x
-7 + 8x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Reorder the terms:
-7 + 8x + -1x2 = 4 + -4 + -4x + 4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-7 + 8x + -1x2 = 0 + -4x + 4x + x2 + -1x2
-7 + 8x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-7 + 8x + -1x2 = 0 + x2 + -1x2
-7 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + 8x + -1x2 = 0

Factor a trinomial.
(-7 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 2
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
Solution
x = {7, 1}

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