2x^2+5x=x^2-4x+10

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Solution for 2x^2+5x=x^2-4x+10 equation: 


Simplifying
2x2 + 5x = x2 + -4x + 10

Reorder the terms:
5x + 2x2 = x2 + -4x + 10

Reorder the terms:
5x + 2x2 = 10 + -4x + x2

Solving
5x + 2x2 = 10 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + 5x + 4x + 2x2 + -1x2 = 10 + -4x + x2 + -10 + 4x + -1x2

Combine like terms: 5x + 4x = 9x
-10 + 9x + 2x2 + -1x2 = 10 + -4x + x2 + -10 + 4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-10 + 9x + 1x2 = 10 + -4x + x2 + -10 + 4x + -1x2

Reorder the terms:
-10 + 9x + 1x2 = 10 + -10 + -4x + 4x + x2 + -1x2

Combine like terms: 10 + -10 = 0
-10 + 9x + 1x2 = 0 + -4x + 4x + x2 + -1x2
-10 + 9x + 1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-10 + 9x + 1x2 = 0 + x2 + -1x2
-10 + 9x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 9x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
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
Solution
x = {-10, 1}

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