7x^2-7x+1=2x^2+4x-1

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Solution for 7x^2-7x+1=2x^2+4x-1 equation: 


Simplifying
7x2 + -7x + 1 = 2x2 + 4x + -1

Reorder the terms:
1 + -7x + 7x2 = 2x2 + 4x + -1

Reorder the terms:
1 + -7x + 7x2 = -1 + 4x + 2x2

Solving
1 + -7x + 7x2 = -1 + 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 1 + -7x + -4x + 7x2 + -2x2 = -1 + 4x + 2x2 + 1 + -4x + -2x2

Combine like terms: 1 + 1 = 2
2 + -7x + -4x + 7x2 + -2x2 = -1 + 4x + 2x2 + 1 + -4x + -2x2

Combine like terms: -7x + -4x = -11x
2 + -11x + 7x2 + -2x2 = -1 + 4x + 2x2 + 1 + -4x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
2 + -11x + 5x2 = -1 + 4x + 2x2 + 1 + -4x + -2x2

Reorder the terms:
2 + -11x + 5x2 = -1 + 1 + 4x + -4x + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
2 + -11x + 5x2 = 0 + 4x + -4x + 2x2 + -2x2
2 + -11x + 5x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
2 + -11x + 5x2 = 0 + 2x2 + -2x2
2 + -11x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + -11x + 5x2 = 0

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


Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

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 = {0.2, 2}

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