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

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


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

Reorder the terms:
(3 + 2x)(2x + -1) = -1(3x + 1)

Reorder the terms:
(3 + 2x)(-1 + 2x) = -1(3x + 1)

Multiply (3 + 2x) * (-1 + 2x)
(3(-1 + 2x) + 2x * (-1 + 2x)) = -1(3x + 1)
((-1 * 3 + 2x * 3) + 2x * (-1 + 2x)) = -1(3x + 1)
((-3 + 6x) + 2x * (-1 + 2x)) = -1(3x + 1)
(-3 + 6x + (-1 * 2x + 2x * 2x)) = -1(3x + 1)
(-3 + 6x + (-2x + 4x2)) = -1(3x + 1)

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 4x + 3x = 7x
-2 + 7x + 4x2 = -1 + -3x + 1 + 3x

Reorder the terms:
-2 + 7x + 4x2 = -1 + 1 + -3x + 3x

Combine like terms: -1 + 1 = 0
-2 + 7x + 4x2 = 0 + -3x + 3x
-2 + 7x + 4x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-2 + 7x + 4x2 = 0

Factor a trinomial.
(-2 + -1x)(1 + -4x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-2, 0.25}

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