x^2-7x+12=3x-4

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Solution for x^2-7x+12=3x-4 equation: 


Simplifying
x2 + -7x + 12 = 3x + -4

Reorder the terms:
12 + -7x + x2 = 3x + -4

Reorder the terms:
12 + -7x + x2 = -4 + 3x

Solving
12 + -7x + x2 = -4 + 3x

Solving for variable 'x'.

Reorder the terms:
12 + 4 + -7x + -3x + x2 = -4 + 3x + 4 + -3x

Combine like terms: 12 + 4 = 16
16 + -7x + -3x + x2 = -4 + 3x + 4 + -3x

Combine like terms: -7x + -3x = -10x
16 + -10x + x2 = -4 + 3x + 4 + -3x

Reorder the terms:
16 + -10x + x2 = -4 + 4 + 3x + -3x

Combine like terms: -4 + 4 = 0
16 + -10x + x2 = 0 + 3x + -3x
16 + -10x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
16 + -10x + x2 = 0

Factor a trinomial.
(2 + -1x)(8 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {2, 8}

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