(3x+4)*(11x-6)=3x+4

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Solution for (3x+4)*(11x-6)=3x+4 equation: 


Simplifying
(3x + 4)(11x + -6) = 3x + 4

Reorder the terms:
(4 + 3x)(11x + -6) = 3x + 4

Reorder the terms:
(4 + 3x)(-6 + 11x) = 3x + 4

Multiply (4 + 3x) * (-6 + 11x)
(4(-6 + 11x) + 3x * (-6 + 11x)) = 3x + 4
((-6 * 4 + 11x * 4) + 3x * (-6 + 11x)) = 3x + 4
((-24 + 44x) + 3x * (-6 + 11x)) = 3x + 4
(-24 + 44x + (-6 * 3x + 11x * 3x)) = 3x + 4
(-24 + 44x + (-18x + 33x2)) = 3x + 4

Combine like terms: 44x + -18x = 26x
(-24 + 26x + 33x2) = 3x + 4

Reorder the terms:
-24 + 26x + 33x2 = 4 + 3x

Solving
-24 + 26x + 33x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
-24 + -4 + 26x + -3x + 33x2 = 4 + 3x + -4 + -3x

Combine like terms: -24 + -4 = -28
-28 + 26x + -3x + 33x2 = 4 + 3x + -4 + -3x

Combine like terms: 26x + -3x = 23x
-28 + 23x + 33x2 = 4 + 3x + -4 + -3x

Reorder the terms:
-28 + 23x + 33x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-28 + 23x + 33x2 = 0 + 3x + -3x
-28 + 23x + 33x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-28 + 23x + 33x2 = 0

Factor a trinomial.
(-4 + -3x)(7 + -11x) = 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 '(7 + -11x)' equal to zero and attempt to solve:

Simplifying
7 + -11x = 0

Solving
7 + -11x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -11x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -11x = 0 + -7
-11x = 0 + -7

Combine like terms: 0 + -7 = -7
-11x = -7

Divide each side by '-11'.
x = 0.6363636364

Simplifying
x = 0.6363636364
Solution
x = {-1.333333333, 0.6363636364}

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