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

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


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

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

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

Multiply (-5 + 2x) * (2 + 3x)
4(-5(2 + 3x) + 2x * (2 + 3x)) = 0
4((2 * -5 + 3x * -5) + 2x * (2 + 3x)) = 0
4((-10 + -15x) + 2x * (2 + 3x)) = 0
4(-10 + -15x + (2 * 2x + 3x * 2x)) = 0
4(-10 + -15x + (4x + 6x2)) = 0

Combine like terms: -15x + 4x = -11x
4(-10 + -11x + 6x2) = 0
(-10 * 4 + -11x * 4 + 6x2 * 4) = 0
(-40 + -44x + 24x2) = 0

Solving
-40 + -44x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -11x + 6x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.6666666667, 2.5}

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