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

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

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

Reorder the terms:
5y(-3 + 4y) = -4y + 3
(-3 * 5y + 4y * 5y) = -4y + 3
(-15y + 20y2) = -4y + 3

Reorder the terms:
-15y + 20y2 = 3 + -4y

Solving
-15y + 20y2 = 3 + -4y

Solving for variable 'y'.

Reorder the terms:
-3 + -15y + 4y + 20y2 = 3 + -4y + -3 + 4y

Combine like terms: -15y + 4y = -11y
-3 + -11y + 20y2 = 3 + -4y + -3 + 4y

Reorder the terms:
-3 + -11y + 20y2 = 3 + -3 + -4y + 4y

Combine like terms: 3 + -3 = 0
-3 + -11y + 20y2 = 0 + -4y + 4y
-3 + -11y + 20y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-3 + -11y + 20y2 = 0

Factor a trinomial.
(-1 + -5y)(3 + -4y) = 0

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

Simplifying
-1 + -5y = 0

Solving
-1 + -5y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5y = 0 + 1
-5y = 0 + 1

Combine like terms: 0 + 1 = 1
-5y = 1

Divide each side by '-5'.
y = -0.2

Simplifying
y = -0.2
Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {-0.2, 0.75}