(2h+3)(h-4)=13

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Solution for (2h+3)(h-4)=13 equation:


Simplifying
(2h + 3)(h + -4) = 13

Reorder the terms:
(3 + 2h)(h + -4) = 13

Reorder the terms:
(3 + 2h)(-4 + h) = 13

Multiply (3 + 2h) * (-4 + h)
(3(-4 + h) + 2h * (-4 + h)) = 13
((-4 * 3 + h * 3) + 2h * (-4 + h)) = 13
((-12 + 3h) + 2h * (-4 + h)) = 13
(-12 + 3h + (-4 * 2h + h * 2h)) = 13
(-12 + 3h + (-8h + 2h2)) = 13

Combine like terms: 3h + -8h = -5h
(-12 + -5h + 2h2) = 13

Solving
-12 + -5h + 2h2 = 13

Solving for variable 'h'.

Reorder the terms:
-12 + -13 + -5h + 2h2 = 13 + -13

Combine like terms: -12 + -13 = -25
-25 + -5h + 2h2 = 13 + -13

Combine like terms: 13 + -13 = 0
-25 + -5h + 2h2 = 0

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

Subproblem 1

Set the factor '(-5 + -2h)' equal to zero and attempt to solve: Simplifying -5 + -2h = 0 Solving -5 + -2h = 0 Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2h = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2h = 0 + 5 -2h = 0 + 5 Combine like terms: 0 + 5 = 5 -2h = 5 Divide each side by '-2'. h = -2.5 Simplifying h = -2.5

Subproblem 2

Set the factor '(5 + -1h)' equal to zero and attempt to solve: Simplifying 5 + -1h = 0 Solving 5 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1h = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1h = 0 + -5 -1h = 0 + -5 Combine like terms: 0 + -5 = -5 -1h = -5 Divide each side by '-1'. h = 5 Simplifying h = 5

Solution

h = {-2.5, 5}

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