2t(t-4)=-3

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Solution for 2t(t-4)=-3 equation:


Simplifying
2t(t + -4) = -3

Reorder the terms:
2t(-4 + t) = -3
(-4 * 2t + t * 2t) = -3
(-8t + 2t2) = -3

Solving
-8t + 2t2 = -3

Solving for variable 't'.

Reorder the terms:
3 + -8t + 2t2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -8t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
1.5 + -4t + t2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4t + -1.5 + t2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4t + t2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4t + t2 = 0 + -1.5
-4t + t2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-4t + t2 = -1.5

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -1.5 + 4

Reorder the terms:
4 + -4t + t2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + -4t + t2 = 2.5

Factor a perfect square on the left side:
(t + -2)(t + -2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(t + -2) equal to 1.58113883 and -1.58113883.

Subproblem 1

t + -2 = 1.58113883 Simplifying t + -2 = 1.58113883 Reorder the terms: -2 + t = 1.58113883 Solving -2 + t = 1.58113883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.58113883 + 2 t = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 t = 3.58113883 Simplifying t = 3.58113883

Subproblem 2

t + -2 = -1.58113883 Simplifying t + -2 = -1.58113883 Reorder the terms: -2 + t = -1.58113883 Solving -2 + t = -1.58113883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.58113883 + 2 t = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 t = 0.41886117 Simplifying t = 0.41886117

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.58113883, 0.41886117}

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