2x^2+3x=x^2+28

Solution for 2x^2+3x=x^2+28 equation:

Simplifying
2x2 + 3x = x2 + 28

Reorder the terms:
3x + 2x2 = x2 + 28

Reorder the terms:
3x + 2x2 = 28 + x2

Solving
3x + 2x2 = 28 + x2

Solving for variable 'x'.

Reorder the terms:
-28 + 3x + 2x2 + -1x2 = 28 + x2 + -28 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-28 + 3x + 1x2 = 28 + x2 + -28 + -1x2

Reorder the terms:
-28 + 3x + 1x2 = 28 + -28 + x2 + -1x2

Combine like terms: 28 + -28 = 0
-28 + 3x + 1x2 = 0 + x2 + -1x2
-28 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + 3x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -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 '(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
Solution
x = {-7, 4}