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

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


Simplifying
3x2 + -1x + -5 = 7x + -9

Reorder the terms:
-5 + -1x + 3x2 = 7x + -9

Reorder the terms:
-5 + -1x + 3x2 = -9 + 7x

Solving
-5 + -1x + 3x2 = -9 + 7x

Solving for variable 'x'.

Reorder the terms:
-5 + 9 + -1x + -7x + 3x2 = -9 + 7x + 9 + -7x

Combine like terms: -5 + 9 = 4
4 + -1x + -7x + 3x2 = -9 + 7x + 9 + -7x

Combine like terms: -1x + -7x = -8x
4 + -8x + 3x2 = -9 + 7x + 9 + -7x

Reorder the terms:
4 + -8x + 3x2 = -9 + 9 + 7x + -7x

Combine like terms: -9 + 9 = 0
4 + -8x + 3x2 = 0 + 7x + -7x
4 + -8x + 3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
4 + -8x + 3x2 = 0

Factor a trinomial.
(2 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
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
Solution
x = {0.6666666667, 2}

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