(5x+3)(8x-4)=0

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Solution for (5x+3)(8x-4)=0 equation: 


Simplifying
(5x + 3)(8x + -4) = 0

Reorder the terms:
(3 + 5x)(8x + -4) = 0

Reorder the terms:
(3 + 5x)(-4 + 8x) = 0

Multiply (3 + 5x) * (-4 + 8x)
(3(-4 + 8x) + 5x * (-4 + 8x)) = 0
((-4 * 3 + 8x * 3) + 5x * (-4 + 8x)) = 0
((-12 + 24x) + 5x * (-4 + 8x)) = 0
(-12 + 24x + (-4 * 5x + 8x * 5x)) = 0
(-12 + 24x + (-20x + 40x2)) = 0

Combine like terms: 24x + -20x = 4x
(-12 + 4x + 40x2) = 0

Solving
-12 + 4x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + x + 10x2) = 0

Factor a trinomial.
4((-3 + -5x)(1 + -2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.6, 0.5}

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