2x^2-x+53=x^2+10x+25

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Solution for 2x^2-x+53=x^2+10x+25 equation: 


Simplifying
2x2 + -1x + 53 = x2 + 10x + 25

Reorder the terms:
53 + -1x + 2x2 = x2 + 10x + 25

Reorder the terms:
53 + -1x + 2x2 = 25 + 10x + x2

Solving
53 + -1x + 2x2 = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
53 + -25 + -1x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 53 + -25 = 28
28 + -1x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: -1x + -10x = -11x
28 + -11x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
28 + -11x + 1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
28 + -11x + 1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
28 + -11x + 1x2 = 0 + 10x + -10x + x2 + -1x2
28 + -11x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
28 + -11x + 1x2 = 0 + x2 + -1x2
28 + -11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + -11x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {4, 7}

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