7x^2+14x=4x^2-32x

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Solution for 7x^2+14x=4x^2-32x equation:


Simplifying
7x2 + 14x = 4x2 + -32x

Reorder the terms:
14x + 7x2 = 4x2 + -32x

Reorder the terms:
14x + 7x2 = -32x + 4x2

Solving
14x + 7x2 = -32x + 4x2

Solving for variable 'x'.

Reorder the terms:
14x + 32x + 7x2 + -4x2 = -32x + 4x2 + 32x + -4x2

Combine like terms: 14x + 32x = 46x
46x + 7x2 + -4x2 = -32x + 4x2 + 32x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
46x + 3x2 = -32x + 4x2 + 32x + -4x2

Reorder the terms:
46x + 3x2 = -32x + 32x + 4x2 + -4x2

Combine like terms: -32x + 32x = 0
46x + 3x2 = 0 + 4x2 + -4x2
46x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
46x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(46 + 3x) = 0

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 '(46 + 3x)' equal to zero and attempt to solve: Simplifying 46 + 3x = 0 Solving 46 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + 3x = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 3x = 0 + -46 3x = 0 + -46 Combine like terms: 0 + -46 = -46 3x = -46 Divide each side by '3'. x = -15.33333333 Simplifying x = -15.33333333

Solution

x = {0, -15.33333333}

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