2x(4+3x)=4x(x-45)

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Solution for 2x(4+3x)=4x(x-45) equation:


Simplifying
2x(4 + 3x) = 4x(x + -45)
(4 * 2x + 3x * 2x) = 4x(x + -45)
(8x + 6x2) = 4x(x + -45)

Reorder the terms:
8x + 6x2 = 4x(-45 + x)
8x + 6x2 = (-45 * 4x + x * 4x)
8x + 6x2 = (-180x + 4x2)

Solving
8x + 6x2 = -180x + 4x2

Solving for variable 'x'.

Reorder the terms:
8x + 180x + 6x2 + -4x2 = -180x + 4x2 + 180x + -4x2

Combine like terms: 8x + 180x = 188x
188x + 6x2 + -4x2 = -180x + 4x2 + 180x + -4x2

Combine like terms: 6x2 + -4x2 = 2x2
188x + 2x2 = -180x + 4x2 + 180x + -4x2

Reorder the terms:
188x + 2x2 = -180x + 180x + 4x2 + -4x2

Combine like terms: -180x + 180x = 0
188x + 2x2 = 0 + 4x2 + -4x2
188x + 2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
188x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(94 + x) = 0

Ignore the factor 2.

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 '(94 + x)' equal to zero and attempt to solve: Simplifying 94 + x = 0 Solving 94 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-94' to each side of the equation. 94 + -94 + x = 0 + -94 Combine like terms: 94 + -94 = 0 0 + x = 0 + -94 x = 0 + -94 Combine like terms: 0 + -94 = -94 x = -94 Simplifying x = -94

Solution

x = {0, -94}

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