(3x-7)(x+1)=-3(x^2+10x+9)

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Solution for (3x-7)(x+1)=-3(x^2+10x+9) equation: 


Simplifying
(3x + -7)(x + 1) = -3(x2 + 10x + 9)

Reorder the terms:
(-7 + 3x)(x + 1) = -3(x2 + 10x + 9)

Reorder the terms:
(-7 + 3x)(1 + x) = -3(x2 + 10x + 9)

Multiply (-7 + 3x) * (1 + x)
(-7(1 + x) + 3x * (1 + x)) = -3(x2 + 10x + 9)
((1 * -7 + x * -7) + 3x * (1 + x)) = -3(x2 + 10x + 9)
((-7 + -7x) + 3x * (1 + x)) = -3(x2 + 10x + 9)
(-7 + -7x + (1 * 3x + x * 3x)) = -3(x2 + 10x + 9)
(-7 + -7x + (3x + 3x2)) = -3(x2 + 10x + 9)

Combine like terms: -7x + 3x = -4x
(-7 + -4x + 3x2) = -3(x2 + 10x + 9)

Reorder the terms:
-7 + -4x + 3x2 = -3(9 + 10x + x2)
-7 + -4x + 3x2 = (9 * -3 + 10x * -3 + x2 * -3)
-7 + -4x + 3x2 = (-27 + -30x + -3x2)

Solving
-7 + -4x + 3x2 = -27 + -30x + -3x2

Solving for variable 'x'.

Reorder the terms:
-7 + 27 + -4x + 30x + 3x2 + 3x2 = -27 + -30x + -3x2 + 27 + 30x + 3x2

Combine like terms: -7 + 27 = 20
20 + -4x + 30x + 3x2 + 3x2 = -27 + -30x + -3x2 + 27 + 30x + 3x2

Combine like terms: -4x + 30x = 26x
20 + 26x + 3x2 + 3x2 = -27 + -30x + -3x2 + 27 + 30x + 3x2

Combine like terms: 3x2 + 3x2 = 6x2
20 + 26x + 6x2 = -27 + -30x + -3x2 + 27 + 30x + 3x2

Reorder the terms:
20 + 26x + 6x2 = -27 + 27 + -30x + 30x + -3x2 + 3x2

Combine like terms: -27 + 27 = 0
20 + 26x + 6x2 = 0 + -30x + 30x + -3x2 + 3x2
20 + 26x + 6x2 = -30x + 30x + -3x2 + 3x2

Combine like terms: -30x + 30x = 0
20 + 26x + 6x2 = 0 + -3x2 + 3x2
20 + 26x + 6x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
20 + 26x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 13x + 3x2) = 0

Factor a trinomial.
2((10 + 3x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 3x)' equal to zero and attempt to solve:

Simplifying
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333

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 = {-3.333333333, -1}

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