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

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


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

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

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

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

Combine like terms: 2x + -35x = -33x
0 = (-10 + -33x + 7x2)

Solving
0 = -10 + -33x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + 10 = 10
10 + 33x + -7x2 = -10 + -33x + 7x2 + 10 + 33x + -7x2

Reorder the terms:
10 + 33x + -7x2 = -10 + 10 + -33x + 33x + 7x2 + -7x2

Combine like terms: -10 + 10 = 0
10 + 33x + -7x2 = 0 + -33x + 33x + 7x2 + -7x2
10 + 33x + -7x2 = -33x + 33x + 7x2 + -7x2

Combine like terms: -33x + 33x = 0
10 + 33x + -7x2 = 0 + 7x2 + -7x2
10 + 33x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
10 + 33x + -7x2 = 0

Factor a trinomial.
(5 + -1x)(2 + 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 '(2 + 7x)' equal to zero and attempt to solve:

Simplifying
2 + 7x = 0

Solving
2 + 7x = 0

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

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

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

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

Divide each side by '7'.
x = -0.2857142857

Simplifying
x = -0.2857142857
Solution
x = {5, -0.2857142857}

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