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

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


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

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

Remove parenthesis around (-5 + 3x)
-5 + 3x = 4x(x + 3)

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

Solving
-5 + 3x = 12x + 4x2

Solving for variable 'x'.

Combine like terms: 3x + -12x = -9x
-5 + -9x + -4x2 = 12x + 4x2 + -12x + -4x2

Reorder the terms:
-5 + -9x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
-5 + -9x + -4x2 = 0 + 4x2 + -4x2
-5 + -9x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + -9x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 9x + 4x2) = 0

Factor a trinomial.
-1((5 + 4x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 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 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25

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 = {-1.25, -1}

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