0=-46x+12+14x^2

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Solution for 0=-46x+12+14x^2 equation: 


Simplifying
0 = -46x + 12 + 14x2

Reorder the terms:
0 = 12 + -46x + 14x2

Solving
0 = 12 + -46x + 14x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + 46x + -14x2 = 12 + -46x + 14x2 + -12 + 46x + -14x2

Reorder the terms:
-12 + 46x + -14x2 = 12 + -12 + -46x + 46x + 14x2 + -14x2

Combine like terms: 12 + -12 = 0
-12 + 46x + -14x2 = 0 + -46x + 46x + 14x2 + -14x2
-12 + 46x + -14x2 = -46x + 46x + 14x2 + -14x2

Combine like terms: -46x + 46x = 0
-12 + 46x + -14x2 = 0 + 14x2 + -14x2
-12 + 46x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
-12 + 46x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 23x + -7x2) = 0

Factor a trinomial.
2((-3 + x)(2 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {3, 0.2857142857}

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