20b^2+15b-43=7

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Solution for 20b^2+15b-43=7 equation:


Simplifying
20b2 + 15b + -43 = 7

Reorder the terms:
-43 + 15b + 20b2 = 7

Solving
-43 + 15b + 20b2 = 7

Solving for variable 'b'.

Reorder the terms:
-43 + -7 + 15b + 20b2 = 7 + -7

Combine like terms: -43 + -7 = -50
-50 + 15b + 20b2 = 7 + -7

Combine like terms: 7 + -7 = 0
-50 + 15b + 20b2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + 3b + 4b2) = 0

Factor a trinomial.
5((-2 + -1b)(5 + -4b)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-2 + -1b)' equal to zero and attempt to solve: Simplifying -2 + -1b = 0 Solving -2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1b = 0 + 2 -1b = 0 + 2 Combine like terms: 0 + 2 = 2 -1b = 2 Divide each side by '-1'. b = -2 Simplifying b = -2

Subproblem 2

Set the factor '(5 + -4b)' equal to zero and attempt to solve: Simplifying 5 + -4b = 0 Solving 5 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4b = 0 + -5 -4b = 0 + -5 Combine like terms: 0 + -5 = -5 -4b = -5 Divide each side by '-4'. b = 1.25 Simplifying b = 1.25

Solution

b = {-2, 1.25}

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