3x(x+5)-5=7+(3+3x)

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Solution for 3x(x+5)-5=7+(3+3x) equation:


Simplifying
3x(x + 5) + -5 = 7 + (3 + 3x)

Reorder the terms:
3x(5 + x) + -5 = 7 + (3 + 3x)
(5 * 3x + x * 3x) + -5 = 7 + (3 + 3x)
(15x + 3x2) + -5 = 7 + (3 + 3x)

Reorder the terms:
-5 + 15x + 3x2 = 7 + (3 + 3x)

Remove parenthesis around (3 + 3x)
-5 + 15x + 3x2 = 7 + 3 + 3x

Combine like terms: 7 + 3 = 10
-5 + 15x + 3x2 = 10 + 3x

Solving
-5 + 15x + 3x2 = 10 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + -10 + 15x + -3x + 3x2 = 10 + 3x + -10 + -3x

Combine like terms: -5 + -10 = -15
-15 + 15x + -3x + 3x2 = 10 + 3x + -10 + -3x

Combine like terms: 15x + -3x = 12x
-15 + 12x + 3x2 = 10 + 3x + -10 + -3x

Reorder the terms:
-15 + 12x + 3x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
-15 + 12x + 3x2 = 0 + 3x + -3x
-15 + 12x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-15 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 4x + x2) = 0

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

Ignore the factor 3.

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 '(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
Solution
x = {-5, 1}

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