5x-5=2(x+1)3x-7

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Solution for 5x-5=2(x+1)3x-7 equation: 


Simplifying
5x + -5 = 2(x + 1) * 3x + -7

Reorder the terms:
-5 + 5x = 2(x + 1) * 3x + -7

Reorder the terms:
-5 + 5x = 2(1 + x) * 3x + -7

Reorder the terms for easier multiplication:
-5 + 5x = 2 * 3x(1 + x) + -7

Multiply 2 * 3
-5 + 5x = 6x(1 + x) + -7
-5 + 5x = (1 * 6x + x * 6x) + -7
-5 + 5x = (6x + 6x2) + -7

Reorder the terms:
-5 + 5x = -7 + 6x + 6x2

Solving
-5 + 5x = -7 + 6x + 6x2

Solving for variable 'x'.

Reorder the terms:
-5 + 7 + 5x + -6x + -6x2 = -7 + 6x + 6x2 + 7 + -6x + -6x2

Combine like terms: -5 + 7 = 2
2 + 5x + -6x + -6x2 = -7 + 6x + 6x2 + 7 + -6x + -6x2

Combine like terms: 5x + -6x = -1x
2 + -1x + -6x2 = -7 + 6x + 6x2 + 7 + -6x + -6x2

Reorder the terms:
2 + -1x + -6x2 = -7 + 7 + 6x + -6x + 6x2 + -6x2

Combine like terms: -7 + 7 = 0
2 + -1x + -6x2 = 0 + 6x + -6x + 6x2 + -6x2
2 + -1x + -6x2 = 6x + -6x + 6x2 + -6x2

Combine like terms: 6x + -6x = 0
2 + -1x + -6x2 = 0 + 6x2 + -6x2
2 + -1x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
2 + -1x + -6x2 = 0

Factor a trinomial.
(1 + -2x)(2 + 3x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0.5, -0.6666666667}

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