2x^2+x-3=7

Solution for 2x^2+x-3=7 equation:

Simplifying
2x2 + x + -3 = 7

Reorder the terms:
-3 + x + 2x2 = 7

Solving
-3 + x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-3 + -7 + x + 2x2 = 7 + -7

Combine like terms: -3 + -7 = -10
-10 + x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-10 + x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(2 + -1x) = 0

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.5, 2}