2(x^2+2x-3)-(x^2+3x)=84

Solution for 2(x^2+2x-3)-(x^2+3x)=84 equation:

Simplifying
2(x2 + 2x + -3) + -1(x2 + 3x) = 84

Reorder the terms:
2(-3 + 2x + x2) + -1(x2 + 3x) = 84
(-3 * 2 + 2x * 2 + x2 * 2) + -1(x2 + 3x) = 84
(-6 + 4x + 2x2) + -1(x2 + 3x) = 84

Reorder the terms:
-6 + 4x + 2x2 + -1(3x + x2) = 84
-6 + 4x + 2x2 + (3x * -1 + x2 * -1) = 84
-6 + 4x + 2x2 + (-3x + -1x2) = 84

Reorder the terms:
-6 + 4x + -3x + 2x2 + -1x2 = 84

Combine like terms: 4x + -3x = 1x
-6 + 1x + 2x2 + -1x2 = 84

Combine like terms: 2x2 + -1x2 = 1x2
-6 + 1x + 1x2 = 84

Solving
-6 + 1x + 1x2 = 84

Solving for variable 'x'.

Reorder the terms:
-6 + -84 + 1x + 1x2 = 84 + -84

Combine like terms: -6 + -84 = -90
-90 + 1x + 1x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-90 + 1x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-10, 9}