3x(x-2)+4=2x^2-1

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Solution for 3x(x-2)+4=2x^2-1 equation: 


Simplifying
3x(x + -2) + 4 = 2x2 + -1

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

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

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

Solving
4 + -6x + 3x2 = -1 + 2x2

Solving for variable 'x'.

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

Combine like terms: 4 + 1 = 5
5 + -6x + 3x2 + -2x2 = -1 + 2x2 + 1 + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
5 + -6x + 1x2 = -1 + 2x2 + 1 + -2x2

Reorder the terms:
5 + -6x + 1x2 = -1 + 1 + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
5 + -6x + 1x2 = 0 + 2x2 + -2x2
5 + -6x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -6x + 1x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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