(3x+4)(x-1)-(3x+4)2=0

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Solution for (3x+4)(x-1)-(3x+4)2=0 equation: 


Simplifying
(3x + 4)(x + -1) + -1(3x + 4) * 2 = 0

Reorder the terms:
(4 + 3x)(x + -1) + -1(3x + 4) * 2 = 0

Reorder the terms:
(4 + 3x)(-1 + x) + -1(3x + 4) * 2 = 0

Multiply (4 + 3x) * (-1 + x)
(4(-1 + x) + 3x * (-1 + x)) + -1(3x + 4) * 2 = 0
((-1 * 4 + x * 4) + 3x * (-1 + x)) + -1(3x + 4) * 2 = 0
((-4 + 4x) + 3x * (-1 + x)) + -1(3x + 4) * 2 = 0
(-4 + 4x + (-1 * 3x + x * 3x)) + -1(3x + 4) * 2 = 0
(-4 + 4x + (-3x + 3x2)) + -1(3x + 4) * 2 = 0

Combine like terms: 4x + -3x = 1x
(-4 + 1x + 3x2) + -1(3x + 4) * 2 = 0

Reorder the terms:
-4 + 1x + 3x2 + -1(4 + 3x) * 2 = 0

Reorder the terms for easier multiplication:
-4 + 1x + 3x2 + -1 * 2(4 + 3x) = 0

Multiply -1 * 2
-4 + 1x + 3x2 + -2(4 + 3x) = 0
-4 + 1x + 3x2 + (4 * -2 + 3x * -2) = 0
-4 + 1x + 3x2 + (-8 + -6x) = 0

Reorder the terms:
-4 + -8 + 1x + -6x + 3x2 = 0

Combine like terms: -4 + -8 = -12
-12 + 1x + -6x + 3x2 = 0

Combine like terms: 1x + -6x = -5x
-12 + -5x + 3x2 = 0

Solving
-12 + -5x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.333333333, 3}

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