(3x+1)(5-2x)-4(3x+1)=0

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Solution for (3x+1)(5-2x)-4(3x+1)=0 equation:


Simplifying
(3x + 1)(5 + -2x) + -4(3x + 1) = 0

Reorder the terms:
(1 + 3x)(5 + -2x) + -4(3x + 1) = 0

Multiply (1 + 3x) * (5 + -2x)
(1(5 + -2x) + 3x * (5 + -2x)) + -4(3x + 1) = 0
((5 * 1 + -2x * 1) + 3x * (5 + -2x)) + -4(3x + 1) = 0
((5 + -2x) + 3x * (5 + -2x)) + -4(3x + 1) = 0
(5 + -2x + (5 * 3x + -2x * 3x)) + -4(3x + 1) = 0
(5 + -2x + (15x + -6x2)) + -4(3x + 1) = 0

Combine like terms: -2x + 15x = 13x
(5 + 13x + -6x2) + -4(3x + 1) = 0

Reorder the terms:
5 + 13x + -6x2 + -4(1 + 3x) = 0
5 + 13x + -6x2 + (1 * -4 + 3x * -4) = 0
5 + 13x + -6x2 + (-4 + -12x) = 0

Reorder the terms:
5 + -4 + 13x + -12x + -6x2 = 0

Combine like terms: 5 + -4 = 1
1 + 13x + -12x + -6x2 = 0

Combine like terms: 13x + -12x = 1x
1 + 1x + -6x2 = 0

Solving
1 + 1x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(1 + 3x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0.5, -0.3333333333}

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