(3x+4)(5x-2)=0

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Solution for (3x+4)(5x-2)=0 equation: 


Simplifying
(3x + 4)(5x + -2) = 0

Reorder the terms:
(4 + 3x)(5x + -2) = 0

Reorder the terms:
(4 + 3x)(-2 + 5x) = 0

Multiply (4 + 3x) * (-2 + 5x)
(4(-2 + 5x) + 3x * (-2 + 5x)) = 0
((-2 * 4 + 5x * 4) + 3x * (-2 + 5x)) = 0
((-8 + 20x) + 3x * (-2 + 5x)) = 0
(-8 + 20x + (-2 * 3x + 5x * 3x)) = 0
(-8 + 20x + (-6x + 15x2)) = 0

Combine like terms: 20x + -6x = 14x
(-8 + 14x + 15x2) = 0

Solving
-8 + 14x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(2 + -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 '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-1.333333333, 0.4}

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