250x^2-343x+81=7x+1+5x^2

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Solution for 250x^2-343x+81=7x+1+5x^2 equation: 


Simplifying
250x2 + -343x + 81 = 7x + 1 + 5x2

Reorder the terms:
81 + -343x + 250x2 = 7x + 1 + 5x2

Reorder the terms:
81 + -343x + 250x2 = 1 + 7x + 5x2

Solving
81 + -343x + 250x2 = 1 + 7x + 5x2

Solving for variable 'x'.

Reorder the terms:
81 + -1 + -343x + -7x + 250x2 + -5x2 = 1 + 7x + 5x2 + -1 + -7x + -5x2

Combine like terms: 81 + -1 = 80
80 + -343x + -7x + 250x2 + -5x2 = 1 + 7x + 5x2 + -1 + -7x + -5x2

Combine like terms: -343x + -7x = -350x
80 + -350x + 250x2 + -5x2 = 1 + 7x + 5x2 + -1 + -7x + -5x2

Combine like terms: 250x2 + -5x2 = 245x2
80 + -350x + 245x2 = 1 + 7x + 5x2 + -1 + -7x + -5x2

Reorder the terms:
80 + -350x + 245x2 = 1 + -1 + 7x + -7x + 5x2 + -5x2

Combine like terms: 1 + -1 = 0
80 + -350x + 245x2 = 0 + 7x + -7x + 5x2 + -5x2
80 + -350x + 245x2 = 7x + -7x + 5x2 + -5x2

Combine like terms: 7x + -7x = 0
80 + -350x + 245x2 = 0 + 5x2 + -5x2
80 + -350x + 245x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
80 + -350x + 245x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(16 + -70x + 49x2) = 0

Factor a trinomial.
5((2 + -7x)(8 + -7x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857

Subproblem 2
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {0.2857142857, 1.142857143}

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