4(x+3)-15=(x+3)(x+3)

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Solution for 4(x+3)-15=(x+3)(x+3) equation:


Simplifying
4(x + 3) + -15 = (x + 3)(x + 3)

Reorder the terms:
4(3 + x) + -15 = (x + 3)(x + 3)
(3 * 4 + x * 4) + -15 = (x + 3)(x + 3)
(12 + 4x) + -15 = (x + 3)(x + 3)

Reorder the terms:
12 + -15 + 4x = (x + 3)(x + 3)

Combine like terms: 12 + -15 = -3
-3 + 4x = (x + 3)(x + 3)

Reorder the terms:
-3 + 4x = (3 + x)(x + 3)

Reorder the terms:
-3 + 4x = (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
-3 + 4x = (3(3 + x) + x(3 + x))
-3 + 4x = ((3 * 3 + x * 3) + x(3 + x))
-3 + 4x = ((9 + 3x) + x(3 + x))
-3 + 4x = (9 + 3x + (3 * x + x * x))
-3 + 4x = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
-3 + 4x = (9 + 6x + x2)

Solving
-3 + 4x = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -9 + 4x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: -3 + -9 = -12
-12 + 4x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 4x + -6x = -2x
-12 + -2x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
-12 + -2x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-12 + -2x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-12 + -2x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-12 + -2x + -1x2 = 0 + x2 + -1x2
-12 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(12 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
12 + 2x + x2 = 0

Solving
12 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 2x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 2x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 2x + x2 = 0 + -12
2x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
2x + x2 = -12

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -12 + 1

Reorder the terms:
1 + 2x + x2 = -12 + 1

Combine like terms: -12 + 1 = -11
1 + 2x + x2 = -11

Factor a perfect square on the left side:
(x + 1)(x + 1) = -11

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.

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