(3x+1)(5x-5)=100

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Solution for (3x+1)(5x-5)=100 equation: 


Simplifying
(3x + 1)(5x + -5) = 100

Reorder the terms:
(1 + 3x)(5x + -5) = 100

Reorder the terms:
(1 + 3x)(-5 + 5x) = 100

Multiply (1 + 3x) * (-5 + 5x)
(1(-5 + 5x) + 3x * (-5 + 5x)) = 100
((-5 * 1 + 5x * 1) + 3x * (-5 + 5x)) = 100
((-5 + 5x) + 3x * (-5 + 5x)) = 100
(-5 + 5x + (-5 * 3x + 5x * 3x)) = 100
(-5 + 5x + (-15x + 15x2)) = 100

Combine like terms: 5x + -15x = -10x
(-5 + -10x + 15x2) = 100

Solving
-5 + -10x + 15x2 = 100

Solving for variable 'x'.

Reorder the terms:
-5 + -100 + -10x + 15x2 = 100 + -100

Combine like terms: -5 + -100 = -105
-105 + -10x + 15x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-105 + -10x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -2x + 3x2) = 0

Factor a trinomial.
5((-7 + -3x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 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 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.333333333, 3}

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