2x^2+7x-35=x^2-5

Solution for 2x^2+7x-35=x^2-5 equation:

Simplifying
2x2 + 7x + -35 = x2 + -5

Reorder the terms:
-35 + 7x + 2x2 = x2 + -5

Reorder the terms:
-35 + 7x + 2x2 = -5 + x2

Solving
-35 + 7x + 2x2 = -5 + x2

Solving for variable 'x'.

Reorder the terms:
-35 + 5 + 7x + 2x2 + -1x2 = -5 + x2 + 5 + -1x2

Combine like terms: -35 + 5 = -30
-30 + 7x + 2x2 + -1x2 = -5 + x2 + 5 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-30 + 7x + 1x2 = -5 + x2 + 5 + -1x2

Reorder the terms:
-30 + 7x + 1x2 = -5 + 5 + x2 + -1x2

Combine like terms: -5 + 5 = 0
-30 + 7x + 1x2 = 0 + x2 + -1x2
-30 + 7x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + 7x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

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

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

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-10, 3}