(4x+7)(x-1)=36x-15

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Solution for (4x+7)(x-1)=36x-15 equation:


Simplifying
(4x + 7)(x + -1) = 36x + -15

Reorder the terms:
(7 + 4x)(x + -1) = 36x + -15

Reorder the terms:
(7 + 4x)(-1 + x) = 36x + -15

Multiply (7 + 4x) * (-1 + x)
(7(-1 + x) + 4x * (-1 + x)) = 36x + -15
((-1 * 7 + x * 7) + 4x * (-1 + x)) = 36x + -15
((-7 + 7x) + 4x * (-1 + x)) = 36x + -15
(-7 + 7x + (-1 * 4x + x * 4x)) = 36x + -15
(-7 + 7x + (-4x + 4x2)) = 36x + -15

Combine like terms: 7x + -4x = 3x
(-7 + 3x + 4x2) = 36x + -15

Reorder the terms:
-7 + 3x + 4x2 = -15 + 36x

Solving
-7 + 3x + 4x2 = -15 + 36x

Solving for variable 'x'.

Reorder the terms:
-7 + 15 + 3x + -36x + 4x2 = -15 + 36x + 15 + -36x

Combine like terms: -7 + 15 = 8
8 + 3x + -36x + 4x2 = -15 + 36x + 15 + -36x

Combine like terms: 3x + -36x = -33x
8 + -33x + 4x2 = -15 + 36x + 15 + -36x

Reorder the terms:
8 + -33x + 4x2 = -15 + 15 + 36x + -36x

Combine like terms: -15 + 15 = 0
8 + -33x + 4x2 = 0 + 36x + -36x
8 + -33x + 4x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
8 + -33x + 4x2 = 0

Factor a trinomial.
(1 + -4x)(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {0.25, 8}

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