2x^2+12x-4=3x+1

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Solution for 2x^2+12x-4=3x+1 equation: 


Simplifying
2x2 + 12x + -4 = 3x + 1

Reorder the terms:
-4 + 12x + 2x2 = 3x + 1

Reorder the terms:
-4 + 12x + 2x2 = 1 + 3x

Solving
-4 + 12x + 2x2 = 1 + 3x

Solving for variable 'x'.

Reorder the terms:
-4 + -1 + 12x + -3x + 2x2 = 1 + 3x + -1 + -3x

Combine like terms: -4 + -1 = -5
-5 + 12x + -3x + 2x2 = 1 + 3x + -1 + -3x

Combine like terms: 12x + -3x = 9x
-5 + 9x + 2x2 = 1 + 3x + -1 + -3x

Reorder the terms:
-5 + 9x + 2x2 = 1 + -1 + 3x + -3x

Combine like terms: 1 + -1 = 0
-5 + 9x + 2x2 = 0 + 3x + -3x
-5 + 9x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + 9x + 2x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -2x) = 0


Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-5, 0.5}

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