7=2x^2-x-3

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

Simplifying
7 = 2x2 + -1x + -3

Reorder the terms:
7 = -3 + -1x + 2x2

Solving
7 = -3 + -1x + 2x2

Solving for variable 'x'.

Combine like terms: 7 + 3 = 10
10 + x + -2x2 = -3 + -1x + 2x2 + 3 + x + -2x2

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

Combine like terms: -3 + 3 = 0
10 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2
10 + x + -2x2 = -1x + x + 2x2 + -2x2

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

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

Factor a trinomial.
(5 + -2x)(2 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

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