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

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


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

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

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

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

Combine like terms: -8x + 15x = 7x
2(-20 + 7x + 6x2) = 0
(-20 * 2 + 7x * 2 + 6x2 * 2) = 0
(-40 + 14x + 12x2) = 0

Solving
-40 + 14x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 7x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-2.5, 1.333333333}

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