(2x-7)(5x+75)=0

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Solution for (2x-7)(5x+75)=0 equation: 


Simplifying
(2x + -7)(5x + 75) = 0

Reorder the terms:
(-7 + 2x)(5x + 75) = 0

Reorder the terms:
(-7 + 2x)(75 + 5x) = 0

Multiply (-7 + 2x) * (75 + 5x)
(-7(75 + 5x) + 2x * (75 + 5x)) = 0
((75 * -7 + 5x * -7) + 2x * (75 + 5x)) = 0
((-525 + -35x) + 2x * (75 + 5x)) = 0
(-525 + -35x + (75 * 2x + 5x * 2x)) = 0
(-525 + -35x + (150x + 10x2)) = 0

Combine like terms: -35x + 150x = 115x
(-525 + 115x + 10x2) = 0

Solving
-525 + 115x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-105 + 23x + 2x2) = 0

Factor a trinomial.
5((-15 + -1x)(7 + -2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-15, 3.5}

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