(4x+5)(6x-3)=0

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Solution for (4x+5)(6x-3)=0 equation: 


Simplifying
(4x + 5)(6x + -3) = 0

Reorder the terms:
(5 + 4x)(6x + -3) = 0

Reorder the terms:
(5 + 4x)(-3 + 6x) = 0

Multiply (5 + 4x) * (-3 + 6x)
(5(-3 + 6x) + 4x * (-3 + 6x)) = 0
((-3 * 5 + 6x * 5) + 4x * (-3 + 6x)) = 0
((-15 + 30x) + 4x * (-3 + 6x)) = 0
(-15 + 30x + (-3 * 4x + 6x * 4x)) = 0
(-15 + 30x + (-12x + 24x2)) = 0

Combine like terms: 30x + -12x = 18x
(-15 + 18x + 24x2) = 0

Solving
-15 + 18x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 6x + 8x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 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 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

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 = {-1.25, 0.5}

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