12x(x+3)+4=5(5x+3)+4

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Solution for 12x(x+3)+4=5(5x+3)+4 equation: 


Simplifying
12x(x + 3) + 4 = 5(5x + 3) + 4

Reorder the terms:
12x(3 + x) + 4 = 5(5x + 3) + 4
(3 * 12x + x * 12x) + 4 = 5(5x + 3) + 4
(36x + 12x2) + 4 = 5(5x + 3) + 4

Reorder the terms:
4 + 36x + 12x2 = 5(5x + 3) + 4

Reorder the terms:
4 + 36x + 12x2 = 5(3 + 5x) + 4
4 + 36x + 12x2 = (3 * 5 + 5x * 5) + 4
4 + 36x + 12x2 = (15 + 25x) + 4

Reorder the terms:
4 + 36x + 12x2 = 15 + 4 + 25x

Combine like terms: 15 + 4 = 19
4 + 36x + 12x2 = 19 + 25x

Solving
4 + 36x + 12x2 = 19 + 25x

Solving for variable 'x'.

Reorder the terms:
4 + -19 + 36x + -25x + 12x2 = 19 + 25x + -19 + -25x

Combine like terms: 4 + -19 = -15
-15 + 36x + -25x + 12x2 = 19 + 25x + -19 + -25x

Combine like terms: 36x + -25x = 11x
-15 + 11x + 12x2 = 19 + 25x + -19 + -25x

Reorder the terms:
-15 + 11x + 12x2 = 19 + -19 + 25x + -25x

Combine like terms: 19 + -19 = 0
-15 + 11x + 12x2 = 0 + 25x + -25x
-15 + 11x + 12x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
-15 + 11x + 12x2 = 0

Factor a trinomial.
(-5 + -3x)(3 + -4x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1.666666667, 0.75}

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