4x^2+10x-18=-8x^2

Solution for 4x^2+10x-18=-8x^2 equation:

Simplifying
4x2 + 10x + -18 = -8x2

Reorder the terms:
-18 + 10x + 4x2 = -8x2

Solving
-18 + 10x + 4x2 = -8x2

Solving for variable 'x'.

Combine like terms: 4x2 + 8x2 = 12x2
-18 + 10x + 12x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-18 + 10x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 5x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 5x + 6x2)' equal to zero and attempt to solve:

Simplifying
-9 + 5x + 6x2 = 0

Solving
-9 + 5x + 6x2 = 0

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

Divide each side by '6'.
-1.5 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.8333333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.8333333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.8333333333x + x2 = 0 + 1.5
0.8333333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.8333333333x + x2 = 1.5

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = 1.5 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 1.5 + 0.1736111111

Combine like terms: 1.5 + 0.1736111111 = 1.6736111111
0.1736111111 + 0.8333333333x + x2 = 1.6736111111

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 1.6736111111

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 1.293681225 and -1.293681225.

Subproblem 1
x + 0.4166666667 = 1.293681225

Simplifying
x + 0.4166666667 = 1.293681225

Reorder the terms:
0.4166666667 + x = 1.293681225

Solving
0.4166666667 + x = 1.293681225

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = 1.293681225 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 1.293681225 + -0.4166666667
x = 1.293681225 + -0.4166666667

Combine like terms: 1.293681225 + -0.4166666667 = 0.8770145583
x = 0.8770145583

Simplifying
x = 0.8770145583

Subproblem 2
x + 0.4166666667 = -1.293681225

Simplifying
x + 0.4166666667 = -1.293681225

Reorder the terms:
0.4166666667 + x = -1.293681225

Solving
0.4166666667 + x = -1.293681225

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = -1.293681225 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -1.293681225 + -0.4166666667
x = -1.293681225 + -0.4166666667

Combine like terms: -1.293681225 + -0.4166666667 = -1.7103478917
x = -1.7103478917

Simplifying
x = -1.7103478917

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8770145583, -1.7103478917}
Solution
x = {0.8770145583, -1.7103478917}