(4x+5)(x-7)=8x+10

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Solution for (4x+5)(x-7)=8x+10 equation: 


Simplifying
(4x + 5)(x + -7) = 8x + 10

Reorder the terms:
(5 + 4x)(x + -7) = 8x + 10

Reorder the terms:
(5 + 4x)(-7 + x) = 8x + 10

Multiply (5 + 4x) * (-7 + x)
(5(-7 + x) + 4x * (-7 + x)) = 8x + 10
((-7 * 5 + x * 5) + 4x * (-7 + x)) = 8x + 10
((-35 + 5x) + 4x * (-7 + x)) = 8x + 10
(-35 + 5x + (-7 * 4x + x * 4x)) = 8x + 10
(-35 + 5x + (-28x + 4x2)) = 8x + 10

Combine like terms: 5x + -28x = -23x
(-35 + -23x + 4x2) = 8x + 10

Reorder the terms:
-35 + -23x + 4x2 = 10 + 8x

Solving
-35 + -23x + 4x2 = 10 + 8x

Solving for variable 'x'.

Reorder the terms:
-35 + -10 + -23x + -8x + 4x2 = 10 + 8x + -10 + -8x

Combine like terms: -35 + -10 = -45
-45 + -23x + -8x + 4x2 = 10 + 8x + -10 + -8x

Combine like terms: -23x + -8x = -31x
-45 + -31x + 4x2 = 10 + 8x + -10 + -8x

Reorder the terms:
-45 + -31x + 4x2 = 10 + -10 + 8x + -8x

Combine like terms: 10 + -10 = 0
-45 + -31x + 4x2 = 0 + 8x + -8x
-45 + -31x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-45 + -31x + 4x2 = 0

Factor a trinomial.
(-5 + -4x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1.25, 9}

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