16b^2=36+36b

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Solution for 16b^2=36+36b equation:


Simplifying
16b2 = 36 + 36b

Solving
16b2 = 36 + 36b

Solving for variable 'b'.

Reorder the terms:
-36 + -36b + 16b2 = 36 + 36b + -36 + -36b

Reorder the terms:
-36 + -36b + 16b2 = 36 + -36 + 36b + -36b

Combine like terms: 36 + -36 = 0
-36 + -36b + 16b2 = 0 + 36b + -36b
-36 + -36b + 16b2 = 36b + -36b

Combine like terms: 36b + -36b = 0
-36 + -36b + 16b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -9b + 4b2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + -4b)' equal to zero and attempt to solve: Simplifying -3 + -4b = 0 Solving -3 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4b = 0 + 3 -4b = 0 + 3 Combine like terms: 0 + 3 = 3 -4b = 3 Divide each side by '-4'. b = -0.75 Simplifying b = -0.75

Subproblem 2

Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3

Solution

b = {-0.75, 3}

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