-h(h-3)+1=4h-1

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Solution for -h(h-3)+1=4h-1 equation:


Simplifying
-1h(h + -3) + 1 = 4h + -1

Reorder the terms:
-1h(-3 + h) + 1 = 4h + -1
(-3 * -1h + h * -1h) + 1 = 4h + -1
(3h + -1h2) + 1 = 4h + -1

Reorder the terms:
1 + 3h + -1h2 = 4h + -1

Reorder the terms:
1 + 3h + -1h2 = -1 + 4h

Solving
1 + 3h + -1h2 = -1 + 4h

Solving for variable 'h'.

Reorder the terms:
1 + 1 + 3h + -4h + -1h2 = -1 + 4h + 1 + -4h

Combine like terms: 1 + 1 = 2
2 + 3h + -4h + -1h2 = -1 + 4h + 1 + -4h

Combine like terms: 3h + -4h = -1h
2 + -1h + -1h2 = -1 + 4h + 1 + -4h

Reorder the terms:
2 + -1h + -1h2 = -1 + 1 + 4h + -4h

Combine like terms: -1 + 1 = 0
2 + -1h + -1h2 = 0 + 4h + -4h
2 + -1h + -1h2 = 4h + -4h

Combine like terms: 4h + -4h = 0
2 + -1h + -1h2 = 0

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

Subproblem 1

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

Subproblem 2

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

Solution

h = {1, -2}

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