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

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


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

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

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

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

Solving
-3 + 7x + 2x2 = -7 + 3x

Solving for variable 'x'.

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

Combine like terms: -3 + 7 = 4
4 + 7x + -3x + 2x2 = -7 + 3x + 7 + -3x

Combine like terms: 7x + -3x = 4x
4 + 4x + 2x2 = -7 + 3x + 7 + -3x

Reorder the terms:
4 + 4x + 2x2 = -7 + 7 + 3x + -3x

Combine like terms: -7 + 7 = 0
4 + 4x + 2x2 = 0 + 3x + -3x
4 + 4x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + 4x + 2x2 = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + 2x + x2)' equal to zero and attempt to solve: Simplifying 2 + 2x + x2 = 0 Solving 2 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2x + x2 = 0 + -2 2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2x + x2 = -2 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 = -2 + 1 Reorder the terms: 1 + 2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + 2x + x2 = -1 Factor a perfect square on the left side: (x + 1)(x + 1) = -1 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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