(0.9t-0.7)(0.11t+1)=0

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Solution for (0.9t-0.7)(0.11t+1)=0 equation:


Simplifying
(0.9t + -0.7)(0.11t + 1) = 0

Reorder the terms:
(-0.7 + 0.9t)(0.11t + 1) = 0

Reorder the terms:
(-0.7 + 0.9t)(1 + 0.11t) = 0

Multiply (-0.7 + 0.9t) * (1 + 0.11t)
(-0.7(1 + 0.11t) + 0.9t * (1 + 0.11t)) = 0
((1 * -0.7 + 0.11t * -0.7) + 0.9t * (1 + 0.11t)) = 0
((-0.7 + -0.077t) + 0.9t * (1 + 0.11t)) = 0
(-0.7 + -0.077t + (1 * 0.9t + 0.11t * 0.9t)) = 0
(-0.7 + -0.077t + (0.9t + 0.099t2)) = 0

Combine like terms: -0.077t + 0.9t = 0.823t
(-0.7 + 0.823t + 0.099t2) = 0

Solving
-0.7 + 0.823t + 0.099t2 = 0

Solving for variable 't'.

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

Divide each side by '0.099'.
-7.070707071 + 8.313131313t + t2 = 0

Move the constant term to the right:

Add '7.070707071' to each side of the equation.
-7.070707071 + 8.313131313t + 7.070707071 + t2 = 0 + 7.070707071

Reorder the terms:
-7.070707071 + 7.070707071 + 8.313131313t + t2 = 0 + 7.070707071

Combine like terms: -7.070707071 + 7.070707071 = 0.000000000
0.000000000 + 8.313131313t + t2 = 0 + 7.070707071
8.313131313t + t2 = 0 + 7.070707071

Combine like terms: 0 + 7.070707071 = 7.070707071
8.313131313t + t2 = 7.070707071

The t term is 8.313131313t.  Take half its coefficient (4.156565657).
Square it (17.27703806) and add it to both sides.

Add '17.27703806' to each side of the equation.
8.313131313t + 17.27703806 + t2 = 7.070707071 + 17.27703806

Reorder the terms:
17.27703806 + 8.313131313t + t2 = 7.070707071 + 17.27703806

Combine like terms: 7.070707071 + 17.27703806 = 24.347745131
17.27703806 + 8.313131313t + t2 = 24.347745131

Factor a perfect square on the left side:
(t + 4.156565657)(t + 4.156565657) = 24.347745131

Calculate the square root of the right side: 4.934343435

Break this problem into two subproblems by setting 
(t + 4.156565657) equal to 4.934343435 and -4.934343435.

Subproblem 1

t + 4.156565657 = 4.934343435 Simplifying t + 4.156565657 = 4.934343435 Reorder the terms: 4.156565657 + t = 4.934343435 Solving 4.156565657 + t = 4.934343435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.156565657' to each side of the equation. 4.156565657 + -4.156565657 + t = 4.934343435 + -4.156565657 Combine like terms: 4.156565657 + -4.156565657 = 0.000000000 0.000000000 + t = 4.934343435 + -4.156565657 t = 4.934343435 + -4.156565657 Combine like terms: 4.934343435 + -4.156565657 = 0.777777778 t = 0.777777778 Simplifying t = 0.777777778

Subproblem 2

t + 4.156565657 = -4.934343435 Simplifying t + 4.156565657 = -4.934343435 Reorder the terms: 4.156565657 + t = -4.934343435 Solving 4.156565657 + t = -4.934343435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.156565657' to each side of the equation. 4.156565657 + -4.156565657 + t = -4.934343435 + -4.156565657 Combine like terms: 4.156565657 + -4.156565657 = 0.000000000 0.000000000 + t = -4.934343435 + -4.156565657 t = -4.934343435 + -4.156565657 Combine like terms: -4.934343435 + -4.156565657 = -9.090909092 t = -9.090909092 Simplifying t = -9.090909092

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.777777778, -9.090909092}

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