(5x+1)(4x-12)=0

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Solution for (5x+1)(4x-12)=0 equation: 


Simplifying
(5x + 1)(4x + -12) = 0

Reorder the terms:
(1 + 5x)(4x + -12) = 0

Reorder the terms:
(1 + 5x)(-12 + 4x) = 0

Multiply (1 + 5x) * (-12 + 4x)
(1(-12 + 4x) + 5x * (-12 + 4x)) = 0
((-12 * 1 + 4x * 1) + 5x * (-12 + 4x)) = 0
((-12 + 4x) + 5x * (-12 + 4x)) = 0
(-12 + 4x + (-12 * 5x + 4x * 5x)) = 0
(-12 + 4x + (-60x + 20x2)) = 0

Combine like terms: 4x + -60x = -56x
(-12 + -56x + 20x2) = 0

Solving
-12 + -56x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -14x + 5x2) = 0

Factor a trinomial.
4((-1 + -5x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

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 = {-0.2, 3}

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