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

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

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

Reorder the terms:
4x(1 + x) = 3(5x + -2)
(1 * 4x + x * 4x) = 3(5x + -2)
(4x + 4x2) = 3(5x + -2)

Reorder the terms:
4x + 4x2 = 3(-2 + 5x)
4x + 4x2 = (-2 * 3 + 5x * 3)
4x + 4x2 = (-6 + 15x)

Solving
4x + 4x2 = -6 + 15x

Solving for variable 'x'.

Reorder the terms:
6 + 4x + -15x + 4x2 = -6 + 15x + 6 + -15x

Combine like terms: 4x + -15x = -11x
6 + -11x + 4x2 = -6 + 15x + 6 + -15x

Reorder the terms:
6 + -11x + 4x2 = -6 + 6 + 15x + -15x

Combine like terms: -6 + 6 = 0
6 + -11x + 4x2 = 0 + 15x + -15x
6 + -11x + 4x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
6 + -11x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.75, 2}