(4x-5)(3x+1)-(6x+2)(x+2)=0

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Solution for (4x-5)(3x+1)-(6x+2)(x+2)=0 equation: 


Simplifying
(4x + -5)(3x + 1) + -1(6x + 2)(x + 2) = 0

Reorder the terms:
(-5 + 4x)(3x + 1) + -1(6x + 2)(x + 2) = 0

Reorder the terms:
(-5 + 4x)(1 + 3x) + -1(6x + 2)(x + 2) = 0

Multiply (-5 + 4x) * (1 + 3x)
(-5(1 + 3x) + 4x * (1 + 3x)) + -1(6x + 2)(x + 2) = 0
((1 * -5 + 3x * -5) + 4x * (1 + 3x)) + -1(6x + 2)(x + 2) = 0
((-5 + -15x) + 4x * (1 + 3x)) + -1(6x + 2)(x + 2) = 0
(-5 + -15x + (1 * 4x + 3x * 4x)) + -1(6x + 2)(x + 2) = 0
(-5 + -15x + (4x + 12x2)) + -1(6x + 2)(x + 2) = 0

Combine like terms: -15x + 4x = -11x
(-5 + -11x + 12x2) + -1(6x + 2)(x + 2) = 0

Reorder the terms:
-5 + -11x + 12x2 + -1(2 + 6x)(x + 2) = 0

Reorder the terms:
-5 + -11x + 12x2 + -1(2 + 6x)(2 + x) = 0

Multiply (2 + 6x) * (2 + x)
-5 + -11x + 12x2 + -1(2(2 + x) + 6x * (2 + x)) = 0
-5 + -11x + 12x2 + -1((2 * 2 + x * 2) + 6x * (2 + x)) = 0
-5 + -11x + 12x2 + -1((4 + 2x) + 6x * (2 + x)) = 0
-5 + -11x + 12x2 + -1(4 + 2x + (2 * 6x + x * 6x)) = 0
-5 + -11x + 12x2 + -1(4 + 2x + (12x + 6x2)) = 0

Combine like terms: 2x + 12x = 14x
-5 + -11x + 12x2 + -1(4 + 14x + 6x2) = 0
-5 + -11x + 12x2 + (4 * -1 + 14x * -1 + 6x2 * -1) = 0
-5 + -11x + 12x2 + (-4 + -14x + -6x2) = 0

Reorder the terms:
-5 + -4 + -11x + -14x + 12x2 + -6x2 = 0

Combine like terms: -5 + -4 = -9
-9 + -11x + -14x + 12x2 + -6x2 = 0

Combine like terms: -11x + -14x = -25x
-9 + -25x + 12x2 + -6x2 = 0

Combine like terms: 12x2 + -6x2 = 6x2
-9 + -25x + 6x2 = 0

Solving
-9 + -25x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -3x)(9 + -2x) = 0


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-0.3333333333, 4.5}

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