(3x+2)(x+1)+(1-3x)(x+5)=0

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Solution for (3x+2)(x+1)+(1-3x)(x+5)=0 equation: 


Simplifying
(3x + 2)(x + 1) + (1 + -3x)(x + 5) = 0

Reorder the terms:
(2 + 3x)(x + 1) + (1 + -3x)(x + 5) = 0

Reorder the terms:
(2 + 3x)(1 + x) + (1 + -3x)(x + 5) = 0

Multiply (2 + 3x) * (1 + x)
(2(1 + x) + 3x * (1 + x)) + (1 + -3x)(x + 5) = 0
((1 * 2 + x * 2) + 3x * (1 + x)) + (1 + -3x)(x + 5) = 0
((2 + 2x) + 3x * (1 + x)) + (1 + -3x)(x + 5) = 0
(2 + 2x + (1 * 3x + x * 3x)) + (1 + -3x)(x + 5) = 0
(2 + 2x + (3x + 3x2)) + (1 + -3x)(x + 5) = 0

Combine like terms: 2x + 3x = 5x
(2 + 5x + 3x2) + (1 + -3x)(x + 5) = 0

Reorder the terms:
2 + 5x + 3x2 + (1 + -3x)(5 + x) = 0

Multiply (1 + -3x) * (5 + x)
2 + 5x + 3x2 + (1(5 + x) + -3x * (5 + x)) = 0
2 + 5x + 3x2 + ((5 * 1 + x * 1) + -3x * (5 + x)) = 0
2 + 5x + 3x2 + ((5 + 1x) + -3x * (5 + x)) = 0
2 + 5x + 3x2 + (5 + 1x + (5 * -3x + x * -3x)) = 0
2 + 5x + 3x2 + (5 + 1x + (-15x + -3x2)) = 0

Combine like terms: 1x + -15x = -14x
2 + 5x + 3x2 + (5 + -14x + -3x2) = 0

Reorder the terms:
2 + 5 + 5x + -14x + 3x2 + -3x2 = 0

Combine like terms: 2 + 5 = 7
7 + 5x + -14x + 3x2 + -3x2 = 0

Combine like terms: 5x + -14x = -9x
7 + -9x + 3x2 + -3x2 = 0

Combine like terms: 3x2 + -3x2 = 0
7 + -9x + 0 = 0
7 + -9x = 0

Solving
7 + -9x = 0

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + -9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9x = 0 + -7
-9x = 0 + -7

Combine like terms: 0 + -7 = -7
-9x = -7

Divide each side by '-9'.
x = 0.7777777778

Simplifying
x = 0.7777777778

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