3-5x(4+5x)=-67

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Solution for 3-5x(4+5x)=-67 equation: 


Simplifying
3 + -5x(4 + 5x) = -67
3 + (4 * -5x + 5x * -5x) = -67
3 + (-20x + -25x2) = -67

Solving
3 + -20x + -25x2 = -67

Solving for variable 'x'.

Reorder the terms:
3 + 67 + -20x + -25x2 = -67 + 67

Combine like terms: 3 + 67 = 70
70 + -20x + -25x2 = -67 + 67

Combine like terms: -67 + 67 = 0
70 + -20x + -25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + -4x + -5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(14 + -4x + -5x2)' equal to zero and attempt to solve:

Simplifying
14 + -4x + -5x2 = 0

Solving
14 + -4x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.8 + 0.8x + x2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + 0.8x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + 0.8x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + 0.8x + x2 = 0 + 2.8
0.8x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
0.8x + x2 = 2.8

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 2.8 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 2.8 + 0.16

Combine like terms: 2.8 + 0.16 = 2.96
0.16 + 0.8x + x2 = 2.96

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 2.96

Calculate the square root of the right side: 1.720465053

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.720465053 and -1.720465053.


Subproblem 1
x + 0.4 = 1.720465053

Simplifying
x + 0.4 = 1.720465053

Reorder the terms:
0.4 + x = 1.720465053

Solving
0.4 + x = 1.720465053

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.720465053 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.720465053 + -0.4
x = 1.720465053 + -0.4

Combine like terms: 1.720465053 + -0.4 = 1.320465053
x = 1.320465053

Simplifying
x = 1.320465053


Subproblem 2
x + 0.4 = -1.720465053

Simplifying
x + 0.4 = -1.720465053

Reorder the terms:
0.4 + x = -1.720465053

Solving
0.4 + x = -1.720465053

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.720465053 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.720465053 + -0.4
x = -1.720465053 + -0.4

Combine like terms: -1.720465053 + -0.4 = -2.120465053
x = -2.120465053

Simplifying
x = -2.120465053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.320465053, -2.120465053}
Solution
x = {1.320465053, -2.120465053}

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