(3x+4)(3x+4)-36=15x+20

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Solution for (3x+4)(3x+4)-36=15x+20 equation: 


Simplifying
(3x + 4)(3x + 4) + -36 = 15x + 20

Reorder the terms:
(4 + 3x)(3x + 4) + -36 = 15x + 20

Reorder the terms:
(4 + 3x)(4 + 3x) + -36 = 15x + 20

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) + -36 = 15x + 20
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) + -36 = 15x + 20
((16 + 12x) + 3x * (4 + 3x)) + -36 = 15x + 20
(16 + 12x + (4 * 3x + 3x * 3x)) + -36 = 15x + 20
(16 + 12x + (12x + 9x2)) + -36 = 15x + 20

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) + -36 = 15x + 20

Reorder the terms:
16 + -36 + 24x + 9x2 = 15x + 20

Combine like terms: 16 + -36 = -20
-20 + 24x + 9x2 = 15x + 20

Reorder the terms:
-20 + 24x + 9x2 = 20 + 15x

Solving
-20 + 24x + 9x2 = 20 + 15x

Solving for variable 'x'.

Reorder the terms:
-20 + -20 + 24x + -15x + 9x2 = 20 + 15x + -20 + -15x

Combine like terms: -20 + -20 = -40
-40 + 24x + -15x + 9x2 = 20 + 15x + -20 + -15x

Combine like terms: 24x + -15x = 9x
-40 + 9x + 9x2 = 20 + 15x + -20 + -15x

Reorder the terms:
-40 + 9x + 9x2 = 20 + -20 + 15x + -15x

Combine like terms: 20 + -20 = 0
-40 + 9x + 9x2 = 0 + 15x + -15x
-40 + 9x + 9x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-40 + 9x + 9x2 = 0

Factor a trinomial.
(-8 + -3x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
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
Solution
x = {-2.666666667, 1.666666667}

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