(3x+4)(5x-1)=0

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Solution for (3x+4)(5x-1)=0 equation: 


Simplifying
(3x + 4)(5x + -1) = 0

Reorder the terms:
(4 + 3x)(5x + -1) = 0

Reorder the terms:
(4 + 3x)(-1 + 5x) = 0

Multiply (4 + 3x) * (-1 + 5x)
(4(-1 + 5x) + 3x * (-1 + 5x)) = 0
((-1 * 4 + 5x * 4) + 3x * (-1 + 5x)) = 0
((-4 + 20x) + 3x * (-1 + 5x)) = 0
(-4 + 20x + (-1 * 3x + 5x * 3x)) = 0
(-4 + 20x + (-3x + 15x2)) = 0

Combine like terms: 20x + -3x = 17x
(-4 + 17x + 15x2) = 0

Solving
-4 + 17x + 15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
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
Solution
x = {-1.333333333, 0.2}

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