2x^2+4x-6=x^2+3x+234

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Solution for 2x^2+4x-6=x^2+3x+234 equation: 


Simplifying
2x2 + 4x + -6 = x2 + 3x + 234

Reorder the terms:
-6 + 4x + 2x2 = x2 + 3x + 234

Reorder the terms:
-6 + 4x + 2x2 = 234 + 3x + x2

Solving
-6 + 4x + 2x2 = 234 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + -234 + 4x + -3x + 2x2 + -1x2 = 234 + 3x + x2 + -234 + -3x + -1x2

Combine like terms: -6 + -234 = -240
-240 + 4x + -3x + 2x2 + -1x2 = 234 + 3x + x2 + -234 + -3x + -1x2

Combine like terms: 4x + -3x = 1x
-240 + 1x + 2x2 + -1x2 = 234 + 3x + x2 + -234 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-240 + 1x + 1x2 = 234 + 3x + x2 + -234 + -3x + -1x2

Reorder the terms:
-240 + 1x + 1x2 = 234 + -234 + 3x + -3x + x2 + -1x2

Combine like terms: 234 + -234 = 0
-240 + 1x + 1x2 = 0 + 3x + -3x + x2 + -1x2
-240 + 1x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-240 + 1x + 1x2 = 0 + x2 + -1x2
-240 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-240 + 1x + 1x2 = 0

Factor a trinomial.
(-16 + -1x)(15 + -1x) = 0


Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-16, 15}

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