x=3x^2-14x+12

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Solution for x=3x^2-14x+12 equation: 


Simplifying
x = 3x2 + -14x + 12

Reorder the terms:
x = 12 + -14x + 3x2

Solving
x = 12 + -14x + 3x2

Solving for variable 'x'.

Reorder the terms:
-12 + x + 14x + -3x2 = 12 + -14x + 3x2 + -12 + 14x + -3x2

Combine like terms: x + 14x = 15x
-12 + 15x + -3x2 = 12 + -14x + 3x2 + -12 + 14x + -3x2

Reorder the terms:
-12 + 15x + -3x2 = 12 + -12 + -14x + 14x + 3x2 + -3x2

Combine like terms: 12 + -12 = 0
-12 + 15x + -3x2 = 0 + -14x + 14x + 3x2 + -3x2
-12 + 15x + -3x2 = -14x + 14x + 3x2 + -3x2

Combine like terms: -14x + 14x = 0
-12 + 15x + -3x2 = 0 + 3x2 + -3x2
-12 + 15x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12 + 15x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 5x + -1x2) = 0

Factor a trinomial.
3((-4 + x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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 = {4, 1}

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