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

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


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

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

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

Multiply (5 + 7x) * (-5 + x)
0 = (5(-5 + x) + 7x * (-5 + x))
0 = ((-5 * 5 + x * 5) + 7x * (-5 + x))
0 = ((-25 + 5x) + 7x * (-5 + x))
0 = (-25 + 5x + (-5 * 7x + x * 7x))
0 = (-25 + 5x + (-35x + 7x2))

Combine like terms: 5x + -35x = -30x
0 = (-25 + -30x + 7x2)

Solving
0 = -25 + -30x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + 25 = 25
25 + 30x + -7x2 = -25 + -30x + 7x2 + 25 + 30x + -7x2

Reorder the terms:
25 + 30x + -7x2 = -25 + 25 + -30x + 30x + 7x2 + -7x2

Combine like terms: -25 + 25 = 0
25 + 30x + -7x2 = 0 + -30x + 30x + 7x2 + -7x2
25 + 30x + -7x2 = -30x + 30x + 7x2 + -7x2

Combine like terms: -30x + 30x = 0
25 + 30x + -7x2 = 0 + 7x2 + -7x2
25 + 30x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
25 + 30x + -7x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(5 + 7x)' equal to zero and attempt to solve:

Simplifying
5 + 7x = 0

Solving
5 + 7x = 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 + 7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7x = 0 + -5
7x = 0 + -5

Combine like terms: 0 + -5 = -5
7x = -5

Divide each side by '7'.
x = -0.7142857143

Simplifying
x = -0.7142857143
Solution
x = {5, -0.7142857143}

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