2x(x+6)=3(x-4)+5

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Solution for 2x(x+6)=3(x-4)+5 equation: 


Simplifying
2x(x + 6) = 3(x + -4) + 5

Reorder the terms:
2x(6 + x) = 3(x + -4) + 5
(6 * 2x + x * 2x) = 3(x + -4) + 5
(12x + 2x2) = 3(x + -4) + 5

Reorder the terms:
12x + 2x2 = 3(-4 + x) + 5
12x + 2x2 = (-4 * 3 + x * 3) + 5
12x + 2x2 = (-12 + 3x) + 5

Reorder the terms:
12x + 2x2 = -12 + 5 + 3x

Combine like terms: -12 + 5 = -7
12x + 2x2 = -7 + 3x

Solving
12x + 2x2 = -7 + 3x

Solving for variable 'x'.

Reorder the terms:
7 + 12x + -3x + 2x2 = -7 + 3x + 7 + -3x

Combine like terms: 12x + -3x = 9x
7 + 9x + 2x2 = -7 + 3x + 7 + -3x

Reorder the terms:
7 + 9x + 2x2 = -7 + 7 + 3x + -3x

Combine like terms: -7 + 7 = 0
7 + 9x + 2x2 = 0 + 3x + -3x
7 + 9x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
7 + 9x + 2x2 = 0

Factor a trinomial.
(7 + 2x)(1 + x) = 0


Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, -1}

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