(20)(5x+5)=(7x)(5x+5)

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Solution for (20)(5x+5)=(7x)(5x+5) equation: 


Simplifying
(20)(5x + 5) = (7x)(5x + 5)

Reorder the terms:
20(5 + 5x) = (7x)(5x + 5)
(5 * 20 + 5x * 20) = (7x)(5x + 5)
(100 + 100x) = (7x)(5x + 5)

Remove parenthesis around (7x)
100 + 100x = 7x(5x + 5)

Reorder the terms:
100 + 100x = 7x(5 + 5x)
100 + 100x = (5 * 7x + 5x * 7x)
100 + 100x = (35x + 35x2)

Solving
100 + 100x = 35x + 35x2

Solving for variable 'x'.

Combine like terms: 100x + -35x = 65x
100 + 65x + -35x2 = 35x + 35x2 + -35x + -35x2

Reorder the terms:
100 + 65x + -35x2 = 35x + -35x + 35x2 + -35x2

Combine like terms: 35x + -35x = 0
100 + 65x + -35x2 = 0 + 35x2 + -35x2
100 + 65x + -35x2 = 35x2 + -35x2

Combine like terms: 35x2 + -35x2 = 0
100 + 65x + -35x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + 13x + -7x2) = 0

Factor a trinomial.
5((20 + -7x)(1 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(20 + -7x)' equal to zero and attempt to solve:

Simplifying
20 + -7x = 0

Solving
20 + -7x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -7x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -7x = 0 + -20
-7x = 0 + -20

Combine like terms: 0 + -20 = -20
-7x = -20

Divide each side by '-7'.
x = 2.857142857

Simplifying
x = 2.857142857

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {2.857142857, -1}

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