(0.5t-.3)(0.07t+1)=0

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Solution for (0.5t-.3)(0.07t+1)=0 equation:


Simplifying
(0.5t + -0.3)(0.07t + 1) = 0

Reorder the terms:
(-0.3 + 0.5t)(0.07t + 1) = 0

Reorder the terms:
(-0.3 + 0.5t)(1 + 0.07t) = 0

Multiply (-0.3 + 0.5t) * (1 + 0.07t)
(-0.3(1 + 0.07t) + 0.5t * (1 + 0.07t)) = 0
((1 * -0.3 + 0.07t * -0.3) + 0.5t * (1 + 0.07t)) = 0
((-0.3 + -0.021t) + 0.5t * (1 + 0.07t)) = 0
(-0.3 + -0.021t + (1 * 0.5t + 0.07t * 0.5t)) = 0
(-0.3 + -0.021t + (0.5t + 0.035t2)) = 0

Combine like terms: -0.021t + 0.5t = 0.479t
(-0.3 + 0.479t + 0.035t2) = 0

Solving
-0.3 + 0.479t + 0.035t2 = 0

Solving for variable 't'.

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

Divide each side by '0.035'.
-8.571428571 + 13.68571429t + t2 = 0

Move the constant term to the right:

Add '8.571428571' to each side of the equation.
-8.571428571 + 13.68571429t + 8.571428571 + t2 = 0 + 8.571428571

Reorder the terms:
-8.571428571 + 8.571428571 + 13.68571429t + t2 = 0 + 8.571428571

Combine like terms: -8.571428571 + 8.571428571 = 0.000000000
0.000000000 + 13.68571429t + t2 = 0 + 8.571428571
13.68571429t + t2 = 0 + 8.571428571

Combine like terms: 0 + 8.571428571 = 8.571428571
13.68571429t + t2 = 8.571428571

The t term is 13.68571429t.  Take half its coefficient (6.842857145).
Square it (46.82469391) and add it to both sides.

Add '46.82469391' to each side of the equation.
13.68571429t + 46.82469391 + t2 = 8.571428571 + 46.82469391

Reorder the terms:
46.82469391 + 13.68571429t + t2 = 8.571428571 + 46.82469391

Combine like terms: 8.571428571 + 46.82469391 = 55.396122481
46.82469391 + 13.68571429t + t2 = 55.396122481

Factor a perfect square on the left side:
(t + 6.842857145)(t + 6.842857145) = 55.396122481

Calculate the square root of the right side: 7.442857145

Break this problem into two subproblems by setting 
(t + 6.842857145) equal to 7.442857145 and -7.442857145.

Subproblem 1

t + 6.842857145 = 7.442857145 Simplifying t + 6.842857145 = 7.442857145 Reorder the terms: 6.842857145 + t = 7.442857145 Solving 6.842857145 + t = 7.442857145 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.842857145' to each side of the equation. 6.842857145 + -6.842857145 + t = 7.442857145 + -6.842857145 Combine like terms: 6.842857145 + -6.842857145 = 0.000000000 0.000000000 + t = 7.442857145 + -6.842857145 t = 7.442857145 + -6.842857145 Combine like terms: 7.442857145 + -6.842857145 = 0.6 t = 0.6 Simplifying t = 0.6

Subproblem 2

t + 6.842857145 = -7.442857145 Simplifying t + 6.842857145 = -7.442857145 Reorder the terms: 6.842857145 + t = -7.442857145 Solving 6.842857145 + t = -7.442857145 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.842857145' to each side of the equation. 6.842857145 + -6.842857145 + t = -7.442857145 + -6.842857145 Combine like terms: 6.842857145 + -6.842857145 = 0.000000000 0.000000000 + t = -7.442857145 + -6.842857145 t = -7.442857145 + -6.842857145 Combine like terms: -7.442857145 + -6.842857145 = -14.28571429 t = -14.28571429 Simplifying t = -14.28571429

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.6, -14.28571429}

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