6x^2-10x+2=7x-3

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Solution for 6x^2-10x+2=7x-3 equation: 


Simplifying
6x2 + -10x + 2 = 7x + -3

Reorder the terms:
2 + -10x + 6x2 = 7x + -3

Reorder the terms:
2 + -10x + 6x2 = -3 + 7x

Solving
2 + -10x + 6x2 = -3 + 7x

Solving for variable 'x'.

Reorder the terms:
2 + 3 + -10x + -7x + 6x2 = -3 + 7x + 3 + -7x

Combine like terms: 2 + 3 = 5
5 + -10x + -7x + 6x2 = -3 + 7x + 3 + -7x

Combine like terms: -10x + -7x = -17x
5 + -17x + 6x2 = -3 + 7x + 3 + -7x

Reorder the terms:
5 + -17x + 6x2 = -3 + 3 + 7x + -7x

Combine like terms: -3 + 3 = 0
5 + -17x + 6x2 = 0 + 7x + -7x
5 + -17x + 6x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
5 + -17x + 6x2 = 0

Factor a trinomial.
(1 + -3x)(5 + -2x) = 0


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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.3333333333, 2.5}

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