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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -5x + -5x = -10x
7 + -10x + 3x2 = -7 + 5x + 7 + -5x

Reorder the terms:
7 + -10x + 3x2 = -7 + 7 + 5x + -5x

Combine like terms: -7 + 7 = 0
7 + -10x + 3x2 = 0 + 5x + -5x
7 + -10x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
7 + -10x + 3x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {1, 2.333333333}

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