(4x+1)(3x-9)=0

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Solution for (4x+1)(3x-9)=0 equation: 


Simplifying
(4x + 1)(3x + -9) = 0

Reorder the terms:
(1 + 4x)(3x + -9) = 0

Reorder the terms:
(1 + 4x)(-9 + 3x) = 0

Multiply (1 + 4x) * (-9 + 3x)
(1(-9 + 3x) + 4x * (-9 + 3x)) = 0
((-9 * 1 + 3x * 1) + 4x * (-9 + 3x)) = 0
((-9 + 3x) + 4x * (-9 + 3x)) = 0
(-9 + 3x + (-9 * 4x + 3x * 4x)) = 0
(-9 + 3x + (-36x + 12x2)) = 0

Combine like terms: 3x + -36x = -33x
(-9 + -33x + 12x2) = 0

Solving
-9 + -33x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -11x + 4x2) = 0

Factor a trinomial.
3((-1 + -4x)(3 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.25, 3}

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