2x^2+3x=x^2+x+35

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Solution for 2x^2+3x=x^2+x+35 equation: 


Simplifying
2x2 + 3x = x2 + x + 35

Reorder the terms:
3x + 2x2 = x2 + x + 35

Reorder the terms:
3x + 2x2 = 35 + x + x2

Solving
3x + 2x2 = 35 + x + x2

Solving for variable 'x'.

Reorder the terms:
-35 + 3x + -1x + 2x2 + -1x2 = 35 + x + x2 + -35 + -1x + -1x2

Combine like terms: 3x + -1x = 2x
-35 + 2x + 2x2 + -1x2 = 35 + x + x2 + -35 + -1x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-35 + 2x + 1x2 = 35 + x + x2 + -35 + -1x + -1x2

Reorder the terms:
-35 + 2x + 1x2 = 35 + -35 + x + -1x + x2 + -1x2

Combine like terms: 35 + -35 = 0
-35 + 2x + 1x2 = 0 + x + -1x + x2 + -1x2
-35 + 2x + 1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
-35 + 2x + 1x2 = 0 + x2 + -1x2
-35 + 2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + 2x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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