(-5x+6)(6x+3)-(6x+3)=0

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


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

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

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

Multiply (6 + -5x) * (3 + 6x)
(6(3 + 6x) + -5x * (3 + 6x)) + -1(6x + 3) = 0
((3 * 6 + 6x * 6) + -5x * (3 + 6x)) + -1(6x + 3) = 0
((18 + 36x) + -5x * (3 + 6x)) + -1(6x + 3) = 0
(18 + 36x + (3 * -5x + 6x * -5x)) + -1(6x + 3) = 0
(18 + 36x + (-15x + -30x2)) + -1(6x + 3) = 0

Combine like terms: 36x + -15x = 21x
(18 + 21x + -30x2) + -1(6x + 3) = 0

Reorder the terms:
18 + 21x + -30x2 + -1(3 + 6x) = 0
18 + 21x + -30x2 + (3 * -1 + 6x * -1) = 0
18 + 21x + -30x2 + (-3 + -6x) = 0

Reorder the terms:
18 + -3 + 21x + -6x + -30x2 = 0

Combine like terms: 18 + -3 = 15
15 + 21x + -6x + -30x2 = 0

Combine like terms: 21x + -6x = 15x
15 + 15x + -30x2 = 0

Solving
15 + 15x + -30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(1 + x + -2x2) = 0

Factor a trinomial.
15((1 + -1x)(1 + 2x)) = 0

Ignore the factor 15.

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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