(7b+3)(4b-12)=0

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Solution for (7b+3)(4b-12)=0 equation:


Simplifying
(7b + 3)(4b + -12) = 0

Reorder the terms:
(3 + 7b)(4b + -12) = 0

Reorder the terms:
(3 + 7b)(-12 + 4b) = 0

Multiply (3 + 7b) * (-12 + 4b)
(3(-12 + 4b) + 7b * (-12 + 4b)) = 0
((-12 * 3 + 4b * 3) + 7b * (-12 + 4b)) = 0
((-36 + 12b) + 7b * (-12 + 4b)) = 0
(-36 + 12b + (-12 * 7b + 4b * 7b)) = 0
(-36 + 12b + (-84b + 28b2)) = 0

Combine like terms: 12b + -84b = -72b
(-36 + -72b + 28b2) = 0

Solving
-36 + -72b + 28b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -18b + 7b2) = 0

Factor a trinomial.
4((-3 + -7b)(3 + -1b)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + -7b)' equal to zero and attempt to solve: Simplifying -3 + -7b = 0 Solving -3 + -7b = 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 + -7b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7b = 0 + 3 -7b = 0 + 3 Combine like terms: 0 + 3 = 3 -7b = 3 Divide each side by '-7'. b = -0.4285714286 Simplifying b = -0.4285714286

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 = {-0.4285714286, 3}

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