-2x+4=2(4x-3)3(-8+4x)

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Solution for -2x+4=2(4x-3)3(-8+4x) equation:


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

Reorder the terms:
4 + -2x = 2(4x + -3) * 3(-8 + 4x)

Reorder the terms:
4 + -2x = 2(-3 + 4x) * 3(-8 + 4x)

Reorder the terms for easier multiplication:
4 + -2x = 2 * 3(-3 + 4x)(-8 + 4x)

Multiply 2 * 3
4 + -2x = 6(-3 + 4x)(-8 + 4x)

Multiply (-3 + 4x) * (-8 + 4x)
4 + -2x = 6(-3(-8 + 4x) + 4x * (-8 + 4x))
4 + -2x = 6((-8 * -3 + 4x * -3) + 4x * (-8 + 4x))
4 + -2x = 6((24 + -12x) + 4x * (-8 + 4x))
4 + -2x = 6(24 + -12x + (-8 * 4x + 4x * 4x))
4 + -2x = 6(24 + -12x + (-32x + 16x2))

Combine like terms: -12x + -32x = -44x
4 + -2x = 6(24 + -44x + 16x2)
4 + -2x = (24 * 6 + -44x * 6 + 16x2 * 6)
4 + -2x = (144 + -264x + 96x2)

Solving
4 + -2x = 144 + -264x + 96x2

Solving for variable 'x'.

Reorder the terms:
4 + -144 + -2x + 264x + -96x2 = 144 + -264x + 96x2 + -144 + 264x + -96x2

Combine like terms: 4 + -144 = -140
-140 + -2x + 264x + -96x2 = 144 + -264x + 96x2 + -144 + 264x + -96x2

Combine like terms: -2x + 264x = 262x
-140 + 262x + -96x2 = 144 + -264x + 96x2 + -144 + 264x + -96x2

Reorder the terms:
-140 + 262x + -96x2 = 144 + -144 + -264x + 264x + 96x2 + -96x2

Combine like terms: 144 + -144 = 0
-140 + 262x + -96x2 = 0 + -264x + 264x + 96x2 + -96x2
-140 + 262x + -96x2 = -264x + 264x + 96x2 + -96x2

Combine like terms: -264x + 264x = 0
-140 + 262x + -96x2 = 0 + 96x2 + -96x2
-140 + 262x + -96x2 = 96x2 + -96x2

Combine like terms: 96x2 + -96x2 = 0
-140 + 262x + -96x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + 131x + -48x2) = 0

Factor a trinomial.
2((-2 + x)(35 + -48x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(35 + -48x)' equal to zero and attempt to solve: Simplifying 35 + -48x = 0 Solving 35 + -48x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -48x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -48x = 0 + -35 -48x = 0 + -35 Combine like terms: 0 + -35 = -35 -48x = -35 Divide each side by '-48'. x = 0.7291666667 Simplifying x = 0.7291666667

Solution

x = {2, 0.7291666667}

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