2x^2+3x=x^2+4

Solution for 2x^2+3x=x^2+4 equation:

Simplifying
2x2 + 3x = x2 + 4

Reorder the terms:
3x + 2x2 = x2 + 4

Reorder the terms:
3x + 2x2 = 4 + x2

Solving
3x + 2x2 = 4 + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 3x + 2x2 + -1x2 = 4 + x2 + -4 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + 3x + 1x2 = 4 + x2 + -4 + -1x2

Reorder the terms:
-4 + 3x + 1x2 = 4 + -4 + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + 3x + 1x2 = 0 + x2 + -1x2
-4 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -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 '(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 = {-4, 1}