(4x-1)(3x+12)=0

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Solution for (4x-1)(3x+12)=0 equation:


Simplifying
(4x + -1)(3x + 12) = 0

Reorder the terms:
(-1 + 4x)(3x + 12) = 0

Reorder the terms:
(-1 + 4x)(12 + 3x) = 0

Multiply (-1 + 4x) * (12 + 3x)
(-1(12 + 3x) + 4x * (12 + 3x)) = 0
((12 * -1 + 3x * -1) + 4x * (12 + 3x)) = 0
((-12 + -3x) + 4x * (12 + 3x)) = 0
(-12 + -3x + (12 * 4x + 3x * 4x)) = 0
(-12 + -3x + (48x + 12x2)) = 0

Combine like terms: -3x + 48x = 45x
(-12 + 45x + 12x2) = 0

Solving
-12 + 45x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 15x + 4x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

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

Solution

x = {-4, 0.25}

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