x(x+7)=2(x+7)*(x-3)+90

Solution for x(x+7)=2(x+7)*(x-3)+90 equation:

Simplifying
x(x + 7) = 2(x + 7)(x + -3) + 90

Reorder the terms:
x(7 + x) = 2(x + 7)(x + -3) + 90
(7 * x + x * x) = 2(x + 7)(x + -3) + 90
(7x + x2) = 2(x + 7)(x + -3) + 90

Reorder the terms:
7x + x2 = 2(7 + x)(x + -3) + 90

Reorder the terms:
7x + x2 = 2(7 + x)(-3 + x) + 90

Multiply (7 + x) * (-3 + x)
7x + x2 = 2(7(-3 + x) + x(-3 + x)) + 90
7x + x2 = 2((-3 * 7 + x * 7) + x(-3 + x)) + 90
7x + x2 = 2((-21 + 7x) + x(-3 + x)) + 90
7x + x2 = 2(-21 + 7x + (-3 * x + x * x)) + 90
7x + x2 = 2(-21 + 7x + (-3x + x2)) + 90

Combine like terms: 7x + -3x = 4x
7x + x2 = 2(-21 + 4x + x2) + 90
7x + x2 = (-21 * 2 + 4x * 2 + x2 * 2) + 90
7x + x2 = (-42 + 8x + 2x2) + 90

Reorder the terms:
7x + x2 = -42 + 90 + 8x + 2x2

Combine like terms: -42 + 90 = 48
7x + x2 = 48 + 8x + 2x2

Solving
7x + x2 = 48 + 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-48 + 7x + -8x + x2 + -2x2 = 48 + 8x + 2x2 + -48 + -8x + -2x2

Combine like terms: 7x + -8x = -1x
-48 + -1x + x2 + -2x2 = 48 + 8x + 2x2 + -48 + -8x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-48 + -1x + -1x2 = 48 + 8x + 2x2 + -48 + -8x + -2x2

Reorder the terms:
-48 + -1x + -1x2 = 48 + -48 + 8x + -8x + 2x2 + -2x2

Combine like terms: 48 + -48 = 0
-48 + -1x + -1x2 = 0 + 8x + -8x + 2x2 + -2x2
-48 + -1x + -1x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-48 + -1x + -1x2 = 0 + 2x2 + -2x2
-48 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-48 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(48 + x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(48 + x + x2)' equal to zero and attempt to solve:

Simplifying
48 + x + x2 = 0

Solving
48 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + x + x2 = 0 + -48
x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
x + x2 = -48

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -48 + 0.25

Reorder the terms:
0.25 + x + x2 = -48 + 0.25

Combine like terms: -48 + 0.25 = -47.75
0.25 + x + x2 = -47.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -47.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.