(4g+3h)(2g+3h)=

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


Simplifying
(4g + 3h)(2g + 3h) = 0

Multiply (4g + 3h) * (2g + 3h)
(4g * (2g + 3h) + 3h * (2g + 3h)) = 0
((2g * 4g + 3h * 4g) + 3h * (2g + 3h)) = 0

Reorder the terms:
((12gh + 8g2) + 3h * (2g + 3h)) = 0
((12gh + 8g2) + 3h * (2g + 3h)) = 0
(12gh + 8g2 + (2g * 3h + 3h * 3h)) = 0
(12gh + 8g2 + (6gh + 9h2)) = 0

Reorder the terms:
(12gh + 6gh + 8g2 + 9h2) = 0

Combine like terms: 12gh + 6gh = 18gh
(18gh + 8g2 + 9h2) = 0

Solving
18gh + 8g2 + 9h2 = 0

Solving for variable 'g'.

Factor a trinomial.
(4g + 3h)(2g + 3h) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(2g + 3h)' equal to zero and attempt to solve: Simplifying 2g + 3h = 0 Solving 2g + 3h = 0 Move all terms containing g to the left, all other terms to the right. Add '-3h' to each side of the equation. 2g + 3h + -3h = 0 + -3h Combine like terms: 3h + -3h = 0 2g + 0 = 0 + -3h 2g = 0 + -3h Remove the zero: 2g = -3h Divide each side by '2'. g = -1.5h Simplifying g = -1.5h

Solution

g = {-0.75h, -1.5h}

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