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

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


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

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

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

Multiply (-4 + 3x) * (-4 + 3x)
(-4(-4 + 3x) + 3x * (-4 + 3x)) + -1(6x + 1)(6x + 1) = 0
((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) + -1(6x + 1)(6x + 1) = 0
((16 + -12x) + 3x * (-4 + 3x)) + -1(6x + 1)(6x + 1) = 0
(16 + -12x + (-4 * 3x + 3x * 3x)) + -1(6x + 1)(6x + 1) = 0
(16 + -12x + (-12x + 9x2)) + -1(6x + 1)(6x + 1) = 0

Combine like terms: -12x + -12x = -24x
(16 + -24x + 9x2) + -1(6x + 1)(6x + 1) = 0

Reorder the terms:
16 + -24x + 9x2 + -1(1 + 6x)(6x + 1) = 0

Reorder the terms:
16 + -24x + 9x2 + -1(1 + 6x)(1 + 6x) = 0

Multiply (1 + 6x) * (1 + 6x)
16 + -24x + 9x2 + -1(1(1 + 6x) + 6x * (1 + 6x)) = 0
16 + -24x + 9x2 + -1((1 * 1 + 6x * 1) + 6x * (1 + 6x)) = 0
16 + -24x + 9x2 + -1((1 + 6x) + 6x * (1 + 6x)) = 0
16 + -24x + 9x2 + -1(1 + 6x + (1 * 6x + 6x * 6x)) = 0
16 + -24x + 9x2 + -1(1 + 6x + (6x + 36x2)) = 0

Combine like terms: 6x + 6x = 12x
16 + -24x + 9x2 + -1(1 + 12x + 36x2) = 0
16 + -24x + 9x2 + (1 * -1 + 12x * -1 + 36x2 * -1) = 0
16 + -24x + 9x2 + (-1 + -12x + -36x2) = 0

Reorder the terms:
16 + -1 + -24x + -12x + 9x2 + -36x2 = 0

Combine like terms: 16 + -1 = 15
15 + -24x + -12x + 9x2 + -36x2 = 0

Combine like terms: -24x + -12x = -36x
15 + -36x + 9x2 + -36x2 = 0

Combine like terms: 9x2 + -36x2 = -27x2
15 + -36x + -27x2 = 0

Solving
15 + -36x + -27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -12x + -9x2) = 0

Factor a trinomial.
3((1 + -3x)(5 + 3x)) = 0

Ignore the factor 3.

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 '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

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

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0.3333333333, -1.666666667}

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