2x(2x+7)=x(x+23)

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Solution for 2x(2x+7)=x(x+23) equation:


Simplifying
2x(2x + 7) = x(x + 23)

Reorder the terms:
2x(7 + 2x) = x(x + 23)
(7 * 2x + 2x * 2x) = x(x + 23)
(14x + 4x2) = x(x + 23)

Reorder the terms:
14x + 4x2 = x(23 + x)
14x + 4x2 = (23 * x + x * x)
14x + 4x2 = (23x + x2)

Solving
14x + 4x2 = 23x + x2

Solving for variable 'x'.

Reorder the terms:
14x + -23x + 4x2 + -1x2 = 23x + x2 + -23x + -1x2

Combine like terms: 14x + -23x = -9x
-9x + 4x2 + -1x2 = 23x + x2 + -23x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-9x + 3x2 = 23x + x2 + -23x + -1x2

Reorder the terms:
-9x + 3x2 = 23x + -23x + x2 + -1x2

Combine like terms: 23x + -23x = 0
-9x + 3x2 = 0 + x2 + -1x2
-9x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-3 + x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

Solution

x = {0, 3}

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