(6x-9)(4x+1)=0

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Solution for (6x-9)(4x+1)=0 equation: 


Simplifying
(6x + -9)(4x + 1) = 0

Reorder the terms:
(-9 + 6x)(4x + 1) = 0

Reorder the terms:
(-9 + 6x)(1 + 4x) = 0

Multiply (-9 + 6x) * (1 + 4x)
(-9(1 + 4x) + 6x * (1 + 4x)) = 0
((1 * -9 + 4x * -9) + 6x * (1 + 4x)) = 0
((-9 + -36x) + 6x * (1 + 4x)) = 0
(-9 + -36x + (1 * 6x + 4x * 6x)) = 0
(-9 + -36x + (6x + 24x2)) = 0

Combine like terms: -36x + 6x = -30x
(-9 + -30x + 24x2) = 0

Solving
-9 + -30x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -10x + 8x2) = 0

Factor a trinomial.
3((-1 + -4x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.25, 1.5}

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