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

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


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

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

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

Multiply (4 + 3x) * (5 + x)
(4(5 + x) + 3x * (5 + x)) = 3(x + 2) + -2
((5 * 4 + x * 4) + 3x * (5 + x)) = 3(x + 2) + -2
((20 + 4x) + 3x * (5 + x)) = 3(x + 2) + -2
(20 + 4x + (5 * 3x + x * 3x)) = 3(x + 2) + -2
(20 + 4x + (15x + 3x2)) = 3(x + 2) + -2

Combine like terms: 4x + 15x = 19x
(20 + 19x + 3x2) = 3(x + 2) + -2

Reorder the terms:
20 + 19x + 3x2 = 3(2 + x) + -2
20 + 19x + 3x2 = (2 * 3 + x * 3) + -2
20 + 19x + 3x2 = (6 + 3x) + -2

Reorder the terms:
20 + 19x + 3x2 = 6 + -2 + 3x

Combine like terms: 6 + -2 = 4
20 + 19x + 3x2 = 4 + 3x

Solving
20 + 19x + 3x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
20 + -4 + 19x + -3x + 3x2 = 4 + 3x + -4 + -3x

Combine like terms: 20 + -4 = 16
16 + 19x + -3x + 3x2 = 4 + 3x + -4 + -3x

Combine like terms: 19x + -3x = 16x
16 + 16x + 3x2 = 4 + 3x + -4 + -3x

Reorder the terms:
16 + 16x + 3x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
16 + 16x + 3x2 = 0 + 3x + -3x
16 + 16x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
16 + 16x + 3x2 = 0

Factor a trinomial.
(4 + x)(4 + 3x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-4, -1.333333333}

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