12x+7=-(2x-3)16x

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Solution for 12x+7=-(2x-3)16x equation:


Simplifying
12x + 7 = -1(2x + -3) * 16x

Reorder the terms:
7 + 12x = -1(2x + -3) * 16x

Reorder the terms:
7 + 12x = -1(-3 + 2x) * 16x

Reorder the terms for easier multiplication:
7 + 12x = -1 * 16x(-3 + 2x)

Multiply -1 * 16
7 + 12x = -16x(-3 + 2x)
7 + 12x = (-3 * -16x + 2x * -16x)
7 + 12x = (48x + -32x2)

Solving
7 + 12x = 48x + -32x2

Solving for variable 'x'.

Combine like terms: 12x + -48x = -36x
7 + -36x + 32x2 = 48x + -32x2 + -48x + 32x2

Reorder the terms:
7 + -36x + 32x2 = 48x + -48x + -32x2 + 32x2

Combine like terms: 48x + -48x = 0
7 + -36x + 32x2 = 0 + -32x2 + 32x2
7 + -36x + 32x2 = -32x2 + 32x2

Combine like terms: -32x2 + 32x2 = 0
7 + -36x + 32x2 = 0

Factor a trinomial.
(1 + -4x)(7 + -8x) = 0

Subproblem 1

Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Subproblem 2

Set the factor '(7 + -8x)' equal to zero and attempt to solve: Simplifying 7 + -8x = 0 Solving 7 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8x = 0 + -7 -8x = 0 + -7 Combine like terms: 0 + -7 = -7 -8x = -7 Divide each side by '-8'. x = 0.875 Simplifying x = 0.875

Solution

x = {0.25, 0.875}

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