(4x+5)(6x-30)=0

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Solution for (4x+5)(6x-30)=0 equation: 


Simplifying
(4x + 5)(6x + -30) = 0

Reorder the terms:
(5 + 4x)(6x + -30) = 0

Reorder the terms:
(5 + 4x)(-30 + 6x) = 0

Multiply (5 + 4x) * (-30 + 6x)
(5(-30 + 6x) + 4x * (-30 + 6x)) = 0
((-30 * 5 + 6x * 5) + 4x * (-30 + 6x)) = 0
((-150 + 30x) + 4x * (-30 + 6x)) = 0
(-150 + 30x + (-30 * 4x + 6x * 4x)) = 0
(-150 + 30x + (-120x + 24x2)) = 0

Combine like terms: 30x + -120x = -90x
(-150 + -90x + 24x2) = 0

Solving
-150 + -90x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-25 + -15x + 4x2) = 0

Factor a trinomial.
6((-5 + -4x)(5 + -1x)) = 0

Ignore the factor 6.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1.25, 5}

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