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

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


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

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

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

Combine like terms: 1x + -7x = -6x
5(7 + -6x + -1x2) = 0
(7 * 5 + -6x * 5 + -1x2 * 5) = 0
(35 + -30x + -5x2) = 0

Solving
35 + -30x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -6x + -1x2) = 0

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

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7
Solution
x = {1, -7}

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