(5x+1)(7-x)=0

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Solution for (5x+1)(7-x)=0 equation: 


Simplifying
(5x + 1)(7 + -1x) = 0

Reorder the terms:
(1 + 5x)(7 + -1x) = 0

Multiply (1 + 5x) * (7 + -1x)
(1(7 + -1x) + 5x * (7 + -1x)) = 0
((7 * 1 + -1x * 1) + 5x * (7 + -1x)) = 0
((7 + -1x) + 5x * (7 + -1x)) = 0
(7 + -1x + (7 * 5x + -1x * 5x)) = 0
(7 + -1x + (35x + -5x2)) = 0

Combine like terms: -1x + 35x = 34x
(7 + 34x + -5x2) = 0

Solving
7 + 34x + -5x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {7, -0.2}

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