x^2-7x+4=3x-5

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Solution for x^2-7x+4=3x-5 equation: 


Simplifying
x2 + -7x + 4 = 3x + -5

Reorder the terms:
4 + -7x + x2 = 3x + -5

Reorder the terms:
4 + -7x + x2 = -5 + 3x

Solving
4 + -7x + x2 = -5 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + 5 + -7x + -3x + x2 = -5 + 3x + 5 + -3x

Combine like terms: 4 + 5 = 9
9 + -7x + -3x + x2 = -5 + 3x + 5 + -3x

Combine like terms: -7x + -3x = -10x
9 + -10x + x2 = -5 + 3x + 5 + -3x

Reorder the terms:
9 + -10x + x2 = -5 + 5 + 3x + -3x

Combine like terms: -5 + 5 = 0
9 + -10x + x2 = 0 + 3x + -3x
9 + -10x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
9 + -10x + x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {1, 9}

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