(4x-6)(2x+5)=0

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Solution for (4x-6)(2x+5)=0 equation: 


Simplifying
(4x + -6)(2x + 5) = 0

Reorder the terms:
(-6 + 4x)(2x + 5) = 0

Reorder the terms:
(-6 + 4x)(5 + 2x) = 0

Multiply (-6 + 4x) * (5 + 2x)
(-6(5 + 2x) + 4x * (5 + 2x)) = 0
((5 * -6 + 2x * -6) + 4x * (5 + 2x)) = 0
((-30 + -12x) + 4x * (5 + 2x)) = 0
(-30 + -12x + (5 * 4x + 2x * 4x)) = 0
(-30 + -12x + (20x + 8x2)) = 0

Combine like terms: -12x + 20x = 8x
(-30 + 8x + 8x2) = 0

Solving
-30 + 8x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 4x + 4x2) = 0

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

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-2.5, 1.5}

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