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

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


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

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

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

Multiply (2 + 4x) * (-5 + 3x)
(2(-5 + 3x) + 4x * (-5 + 3x)) = 0
((-5 * 2 + 3x * 2) + 4x * (-5 + 3x)) = 0
((-10 + 6x) + 4x * (-5 + 3x)) = 0
(-10 + 6x + (-5 * 4x + 3x * 4x)) = 0
(-10 + 6x + (-20x + 12x2)) = 0

Combine like terms: 6x + -20x = -14x
(-10 + -14x + 12x2) = 0

Solving
-10 + -14x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -7x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-0.5, 1.666666667}

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