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

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


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

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

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

Multiply (5 + 6x) * (-1 + 3x)
(5(-1 + 3x) + 6x * (-1 + 3x)) = 4
((-1 * 5 + 3x * 5) + 6x * (-1 + 3x)) = 4
((-5 + 15x) + 6x * (-1 + 3x)) = 4
(-5 + 15x + (-1 * 6x + 3x * 6x)) = 4
(-5 + 15x + (-6x + 18x2)) = 4

Combine like terms: 15x + -6x = 9x
(-5 + 9x + 18x2) = 4

Solving
-5 + 9x + 18x2 = 4

Solving for variable 'x'.

Reorder the terms:
-5 + -4 + 9x + 18x2 = 4 + -4

Combine like terms: -5 + -4 = -9
-9 + 9x + 18x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-9 + 9x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-1 + x + 2x2) = 0

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

Ignore the factor 9.

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1, 0.5}

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