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

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


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

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

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

Multiply (1 + 3x) * (-4 + 5x)
(1(-4 + 5x) + 3x * (-4 + 5x)) = 0
((-4 * 1 + 5x * 1) + 3x * (-4 + 5x)) = 0
((-4 + 5x) + 3x * (-4 + 5x)) = 0
(-4 + 5x + (-4 * 3x + 5x * 3x)) = 0
(-4 + 5x + (-12x + 15x2)) = 0

Combine like terms: 5x + -12x = -7x
(-4 + -7x + 15x2) = 0

Solving
-4 + -7x + 15x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-0.3333333333, 0.8}

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