4y(y-3)=16

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Solution for 4y(y-3)=16 equation:


Simplifying
4y(y + -3) = 16

Reorder the terms:
4y(-3 + y) = 16
(-3 * 4y + y * 4y) = 16
(-12y + 4y2) = 16

Solving
-12y + 4y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + -12y + 4y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -12y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -3y + y2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + -1y)' equal to zero and attempt to solve: Simplifying -1 + -1y = 0 Solving -1 + -1y = 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 + -1y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1y = 0 + 1 -1y = 0 + 1 Combine like terms: 0 + 1 = 1 -1y = 1 Divide each side by '-1'. y = -1 Simplifying y = -1

Subproblem 2

Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4

Solution

y = {-1, 4}

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