3x^2-9x-7=5x-7

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Solution for 3x^2-9x-7=5x-7 equation: 


Simplifying
3x2 + -9x + -7 = 5x + -7

Reorder the terms:
-7 + -9x + 3x2 = 5x + -7

Reorder the terms:
-7 + -9x + 3x2 = -7 + 5x

Add '7' to each side of the equation.
-7 + -9x + 7 + 3x2 = -7 + 7 + 5x

Reorder the terms:
-7 + 7 + -9x + 3x2 = -7 + 7 + 5x

Combine like terms: -7 + 7 = 0
0 + -9x + 3x2 = -7 + 7 + 5x
-9x + 3x2 = -7 + 7 + 5x

Combine like terms: -7 + 7 = 0
-9x + 3x2 = 0 + 5x
-9x + 3x2 = 5x

Solving
-9x + 3x2 = 5x

Solving for variable 'x'.

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

Combine like terms: -9x + -5x = -14x
-14x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-14x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-14 + 3x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-14 + 3x)' equal to zero and attempt to solve:

Simplifying
-14 + 3x = 0

Solving
-14 + 3x = 0

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

Add '14' to each side of the equation.
-14 + 14 + 3x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3x = 0 + 14
3x = 0 + 14

Combine like terms: 0 + 14 = 14
3x = 14

Divide each side by '3'.
x = 4.666666667

Simplifying
x = 4.666666667
Solution
x = {0, 4.666666667}

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