(2x+1)(5-6x)=3x(4x-1)

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Solution for (2x+1)(5-6x)=3x(4x-1) equation:


Simplifying
(2x + 1)(5 + -6x) = 3x(4x + -1)

Reorder the terms:
(1 + 2x)(5 + -6x) = 3x(4x + -1)

Multiply (1 + 2x) * (5 + -6x)
(1(5 + -6x) + 2x * (5 + -6x)) = 3x(4x + -1)
((5 * 1 + -6x * 1) + 2x * (5 + -6x)) = 3x(4x + -1)
((5 + -6x) + 2x * (5 + -6x)) = 3x(4x + -1)
(5 + -6x + (5 * 2x + -6x * 2x)) = 3x(4x + -1)
(5 + -6x + (10x + -12x2)) = 3x(4x + -1)

Combine like terms: -6x + 10x = 4x
(5 + 4x + -12x2) = 3x(4x + -1)

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

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

Solving for variable 'x'.

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

Combine like terms: 4x + 3x = 7x
5 + 7x + -12x2 + -12x2 = -3x + 12x2 + 3x + -12x2

Combine like terms: -12x2 + -12x2 = -24x2
5 + 7x + -24x2 = -3x + 12x2 + 3x + -12x2

Reorder the terms:
5 + 7x + -24x2 = -3x + 3x + 12x2 + -12x2

Combine like terms: -3x + 3x = 0
5 + 7x + -24x2 = 0 + 12x2 + -12x2
5 + 7x + -24x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
5 + 7x + -24x2 = 0

Factor a trinomial.
(5 + -8x)(1 + 3x) = 0


Subproblem 1
Set the factor '(5 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 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 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625

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 = {0.625, -0.3333333333}

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