h(x)=(x-5)(x+4)f(1)

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Solution for h(x)=(x-5)(x+4)f(1) equation:


Simplifying
h(x) = (x + -5)(x + 4) * f(1)

Multiply h * x
hx = (x + -5)(x + 4) * f(1)

Reorder the terms:
hx = (-5 + x)(x + 4) * f(1)

Reorder the terms:
hx = (-5 + x)(4 + x) * f(1)

Reorder the terms for easier multiplication:
hx = 1f(-5 + x)(4 + x)

Multiply (-5 + x) * (4 + x)
hx = 1f(-5(4 + x) + x(4 + x))
hx = 1f((4 * -5 + x * -5) + x(4 + x))
hx = 1f((-20 + -5x) + x(4 + x))
hx = 1f(-20 + -5x + (4 * x + x * x))
hx = 1f(-20 + -5x + (4x + x2))

Combine like terms: -5x + 4x = -1x
hx = 1f(-20 + -1x + x2)
hx = (-20 * 1f + -1x * 1f + x2 * 1f)
hx = (-20f + -1fx + 1fx2)

Solving
hx = -20f + -1fx + 1fx2

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Divide each side by 'x'.
h = -20fx-1 + -1f + fx

Simplifying
h = -20fx-1 + -1f + fx

Reorder the terms:
h = -1f + -20fx-1 + fx

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